Dissertationen zum Thema „MODIFIED THEORIES“

The recent observational data in cosmology seem to indicate that the universe is currently expanding in an accelerated way. This unexpected conclusion can be explained assuming the presence of a non-vanishing yet extremely fine tuned cosmological constant, or invoking the existence of an exotic source of energy, dark energy, which is not observed in laboratory experiments yet seems to dominate the energy budget of the Universe. On the other hand, it may be that these observations are just signalling the fact that Einstein's General Relativity is not the correct description of gravity when we consider distances of the order of the present horizon of the universe. In order to study if the latter explanation is correct, we have to formulate new theories of the gravitational interaction, and see if they admit cosmological solutions which fit the observational data in a satisfactory way. Quite generally, modifying General Relativity introduces new degrees of freedom, which are responsible for the different large distance behaviour. On one hand, often these new degrees of freedom have negative kinetic energy, which implies that the theory is plagued by ghost instabilities. On the other hand, for a modified gravity theory to be phenomenologically viable it is necessary that the extra degrees of freedom are efficiently screened on terrestrial and astrophysical scales. One of the known mechanisms which can screen the extra degrees of freedom is the Vainshtein mechanism, which involves derivative self-interaction terms for these degrees of freedom. In this thesis, we consider two different models, the Cascading DGP and the dRGT massive gravity, which are candidates for viable models to modify gravity at very large distances. Regarding the Cascading DGP model, we consider the minimal (6D) set-up and we perform a perturbative analysis at first order of the behaviour of the gravitational field and of the branes position around background solutions where pure tension is localized on the 4D brane. We consider a specific realization of this set-up where the 5D brane can be considered thin with respect to the 4D one. We show that the thin limit of the 4D brane inside the (already thin) 5D brane is well defined, at least for the configurations that we consider, and confirm that the gravitational field on the 4D brane is finite for a general choice of the energymomentum tensor. We also confirm that there exists a critical tension which separates background configurations which possess a ghost among the perturbation modes, and background configurations which are ghost-free. We find a value for the critical tension which is different from the value which has been obtained in the literature; we comment on the difference between these two results, and perform a numeric calculation in a particular case where the exact solution is known to support the validity of our analysis. Regarding the dRGT massive gravity, we consider the static and spherically symmetric solutions of these theories, and we investigate the effectiveness of the Vainshtein screening mechanism. We focus on the branch of solutions in which the Vainshtein mechanism can occur, and we truncate the analysis to scales below the gravitational Compton wavelength, and consider the weak field limit for the gravitational potentials, while keeping all non-linearities of the mode which is involved in the screening. We determine analytically the number and properties of local solutions which exist asymptotically on large scales, and of local (inner) solutions which exist on small scales. Moreover, we analyze in detail in which cases the solutions match in an intermediate region. We show that asymptotically flat solutions connect only to inner configurations displaying the Vainshtein mechanism, while non asymptotically flat solutions can connect both with inner solutions which display the Vainshtein mechanism, or with solutions which display a self-shielding behaviour of the gravitational field. We show furthermore that there are some regions in the parameter space of the theory where global solutions do not exist, and characterize precisely in which regions the Vainshtein mechanism takes place.

The recent observational data in cosmology seem to indicate that the universe is currently expanding in an accelerated way. This unexpected conclusion can be explained assuming the presence of a non-vanishing yet extremely fine tuned cosmological constant, or invoking the existence of an exotic source of energy, dark energy, which is not observed in laboratory experiments yet seems to dominate the energy budget of the Universe. On the other hand, it may be that these observations are just signalling the fact that Einstein's General Relativity is not the correct description of gravity when we consider distances of the order of the present horizon of the universe. In order to study if the latter explanation is correct, we have to formulate new theories of the gravitational interaction, and see if they admit cosmological solutions which fit the observational data in a satisfactory way. A necessary condition for the viability of a theory of ``modified gravity'' is that it has to reproduce to high precision the results of General Relativity in experimental setups where the latter is well tested. Quite in general, modifying General Relativity introduces new degrees of freedom, which are responsible for the different large distance behavior. For a modified gravity theory to be phenomenologically viable, it is necessary that the extra degrees of freedom are efficiently screened on terrestrial and astrophysical scales. One of the known mechanisms which can screen the extra degrees of freedom is known as the Vainshtein mechanism, which involves derivative self-interaction terms for these degrees of freedom. In this thesis, we consider a class of nonlinear massive gravity theories known as dGRT Massive Gravity. These theories are candidates as viable models to modify gravity at very large distances, and, apart from the mass, they contain two free parameters. We investigate the effectiveness of the Vainshtein screening mechanism in this class of theories. There are two branches of static and spherically symmetric solutions, and we consider only the branch in which the Vainshtein mechanism can occur. We truncate the analysis to scales below the gravitational Compton wavelength, and consider the weak f\mbox{}ield limit for the gravitational potentials, while keeping all non-linearities of the mode which is involved in the screening. We determine analytically the number and properties of local solutions which exist asymptotically on large scales, and of local (inner) solutions which exist on small scales. We analyze in detail in which cases the solutions match in an intermediate region. Asymptotically flat solutions connect only to inner configurations displaying the Vainshtein mechanism, while non asymptotically flat solutions can connect both with inner solutions which display the Vainshtein mechanism, or with solutions which display a self-shielding behaviour of the gravitational field. We show furthermore that there are some regions in the parameter space where global solutions do not exist, and characterise precisely in which regions of the phase space the Vainshtein mechanism takes place.

Teleparallel gravity is an alternative formulation of gravity which has the same field equations as General Relativity (GR), therefore, it is also known as the Teleparallel equivalent of General Relativity (TEGR). This theory is a gauge theory of the translations with the torsion tensor being non-zero but with a vanishing curvature tensor, hence, the manifold is globally flat. An interesting approach for understanding the late-time accelerating behaviour of the Universe is called modified gravity where GR is extended or modified. In the same spirit, since TEGR is equivalent to GR, one can consider its modifications and study if they can describe the current cosmological observations. This thesis is devoted to studying several modified Teleparallel theories of gravity with emphasis on late-time cosmology. Those Teleparallel theories are in general different to the modified theories based on GR, but one can relate and classify them accordingly. Various Teleparallel theories are presented and studied such as Teleparallel scalar-tensor theories, quintom models, Teleparallel non-local gravity, and f(T,B) gravity and its extensions (coupled with matter, extensions of new GR and Gauss-Bonnet) where T is the scalar torsion and B is the boundary term which is related with the Ricci scalar via R=-T+B.

This thesis studies the viability of classes of modified gravity (MG) theories based on generalisations of the Einstein-Hilbert action. Particular emphasis is given to f(R) theories in both the metric and Palatini formalisms, scalar-tensor theories and generalised Gauss-Bonnet theories. An urgent task at present is to devise stringent tests in order to reduce the range of candidate models based on these theories. In this thesis a detailed study is made of the viability of these models using constraints from requirement of stability, background cosmological dynamics, local gravity constraints (LGC) and matter density perturbations. In each case the conditions required for stability and viability of the background dynamics are presented. In the case of generalised Gauss-Bonnet theories the circumstances leading to the existence and stability of cosmological scaling solutions are established. In the scalar-tensor theories considered here, which includes metric-f(R) theories as a special case, there is a strong coupling of the scalar field to matter in the Einstein frame which violates all LGC. It is shown that using a chameleon mechanism, models that are compatible with LGC may be constructed. It is found that such models, which are also consistent with background dynamics, are constrained to be close to the CDMmodel during the radiation/matter epochs and can lead to the divergence of the equation of state of dark energy. In contrast, such constraints only impose mild restrictions on Palatini-f(R) models. Still more stringent constraints are provided by studying matter density perturbations. In particular, it is shown that the unconventional evolution of perturbations in the Palatini formalism leads to f(R) models in this case to be practically identical to the CDM model. For each case it is also shown that (for viable models) matter perturbation equations derived under a sub-horizon approximation are reliable even for super-Hubble scales provided the oscillating mode does not dominate over the matter-induced mode. Such approximate equations are especially reliable in the Palatini formalism, where the oscillating mode is absent. In summary, the analyses carried out in this thesis suggest that subjectingMG theories to observational constraints confines the viable range of models to be very close to (and in some cases indistinguishable from) the CDM model.

Einstein’s equations are derived by following Jacobson’s thermodynamic method. It is seen that a family of possible field equations exist which satisfy the thermodynamic argument. Modified theories of gravity are addressed as possible candidates for replacing dark matter as an explanation for anomalous cosmological phenomena. Many of the proposed modified theories are not powerful enough to explain the currently observed phenomena and are rejected as viable theories of gravity. A surviving candidate, TeVeS, is further analyzed under the aforementioned thermodynamic argument to check for its consistency with thermodynamics.

It is now a consolidated fact that our Universe is undergoing an accelerated expansion. According to Einstein's General Relativity, if the main constituents of our Universe were ordinary and cold dark matter, then we would expect it to be contracting and collapsing due to matter's attractive nature. The simplest explanation we have for this acceleration is in the form of a component with a negative ratio of pressure to density equal to -1 known as cosmological constant, Λ , presently dominating over baryonic and cold dark matter. However, the Λ Cold Dark Matter (Λ CDM) model suffers from a well known fine tuning problem. This led to the formulation of dark energy and modified gravity theories as alternatives to the problem of cosmic acceleration. These theories either include additional degrees of freedom, higher-order equations of motion, extra dimensionalities or imply non-locality. In this thesis we focus on single field scalar tensor theories embedded within Horndeski gravity. Even though there is currently doubt on their ability to explain cosmic acceleration without having a bare cosmological constant on their action, the degree of freedom they introduce mediates an additional fifth force. And while this force has to suppressed on Solar system scales, it can have interesting and observable effects on cosmological scales. Over the next decade there is a surge of surveys that will improve the understanding of our Universe on the largest scales. Hence, in this work, we take several different modified gravity theories and study their impact on cosmological observables. We will analyze the dynamics of linear perturbations on these theories and clearly highlight how they deviate from Λ CDM, allowing to break the degeneracy at the background level. We will also study the evolution of the gravitational potentials on sub horizon scales and provide simplified expressions at this regime and, for some models, obtain constraints using the latest data.

Our theoretical understanding of the dynamical evolution of the Universe has certainly improved during the recently established era of precision cosmology. However, the nature of the dark sector remains the greatest puzzle in cosmology. Although we re–establish that the concordance model of cosmology is in agreement with current cosmological observations, this simplistic model is unequivocally theoretically unappealing. Thence, we investigate a number of alternative cosmological models and illustrate their distinctive cosmological consequences. For instance, we consider a scalar–tensor theory of gravitation, such that the minimally coupled scalar field is explicitly coupled to multiple fluid components. The assumed coupling functions are specified by the theoretically well–motivated conformal and disformal coupling functions. We perform a dynamical systems analysis, in which we establish the existence and stability conditions for every fixed point, and illustrate that disformally coupled systems have a dissimilar cosmological evolution with respect to the conformally coupled and uncoupled systems. We further show that a disformal coupling between the matter and radiation sectors is characterised by a varying fine–structure constant. Moreover, a direct coupling between dark energy and dark matter is not theoretically forbidden and might be incorporated in extensions of the standard model of particle physics. We consider a coupled quintessence model, in which the dark energy scalar field only couples to dark matter via the conformal and disformal coupling functions, and is decoupled from the conventional baryonic matter sector. We scrutinise the distinctive features of this cosmological model, where we particularly show that when the dark sector constituents are disformally coupled, intermediate–scales and time–dependent damped oscillations appear in the matter growth rate function. We confront this coupled quintessence model with current cosmological data sets, and illustrate that Nature is consistent with a null coupling within the dark sector of the Universe.

The aim of this work is to investigate the both, some mathematical and physical general aspect of modified gravity, and, more specifically, the proprieties of viable, realistic models of modified gravity which can be used to reproduce the inflation and the dark energy epoch of universe today.

The aim of this work is to investigate the both, some mathematical and physical general aspect of modified gravity, and, more specifically, the proprieties of viable, realistic models of modified gravity which can be used to reproduce the inflation and the dark energy epoch of universe today.

Matter-wave interferometry is ideal for detecting small forces, being able to sense changes of acceleration as small as 1 nm s^-2 as a result of quantum interference. In this thesis, I prepare a cloud of ultracold Rb-87 atoms and measure the force between an atom and a cm-sized source mass using atom interferometry. The interferometer uses a sequence of optical Raman pulses to split, reflect, and recombine the atomic wavefunction. The force that is measured is consistent with standard Newtonian gravity. Some theories that have been advanced to explain the accelerating expansion of the universe - otherwise known as dark energy - predict a departure from the Newtonian force in my experiment. I use my result to constrain the parameters of these theories. The sensitivity of the experiment is sufficient to probe physics at energies approaching the Planck scale.

Dans cette thèse, nous étudions deux aspects de la théorie de la gravitation : la correspondance holographique et les théories de la gravité modifiée. La correspondance holographique est une conjecture remarquable qui établit l'équivalence entre certaines théories de la gravitation et certaines théories quantiques des champs. Les recherches dans le domaine de la gravité modifiée portent sur le développement des théories cohérentes de la gravité qui diffèrent de la relativité générale d'Einstein. La première partie de la thèse est dédiée à la correspondance holographique, ou la dualité gauge/gravité. Nous présentons un nouveau formalisme pour étudier les théories d'Einstein- scalaires du point de vue de l'holographie. Nous appliquons ce formalisme à la théorie holographique duale à une théorie de Yang- Mills à quatre dimensions. Nous calculons holographiquement l'action efficace pour le condensat de gluons, ainsi que pour la version de cet operateur qui est invariant sous le groupe de renormalisation. La deuxième partie de cette thèse traite les théories de la gravité modifiée. Nous nous concentrons sur une limite intéressante de la gravité massive autour de l'espace de Sitter. La théorie est connue comme gravité partiellement massless. Nous abordons la question s'il existe une extension non-linéaire de la gravité partiellement massless
In this thesis, we will investigate two aspects of gravitational theories: holographic correspondence and modified gravity theories. Holographic correspondence is a remarkable conjecture which establishes the equivalence between certain gravitational theories and certain quantum field theories. The research in the domain of modified gravity concerns the development of consistent theories of gravity that are different from the standard general relativity. The first part of this thesis is dedicated to the holographic correspondence or the gauge/gravity duality. We will present a novel formalism to study the Einstein-scalar theories from the perspective of holography. We will apply this novel formalism to holographic Yang-Mills theory. We will compute the effective action for the gluon condensate and its relative that is renormalization-roup invariant. The second part of this thesis is about modified theories of gravity. We will focus on an interesting limit of massive gravity around de Sitter space. The theory is known as partially massless gravity. We will investigate whether a non-linear extension for partially massless gravity exists

En esta memoria de tesis se expone el trabajo llevado a cabo por el doctorando durante los últimos cuatro años, el cual versa principalmente sobre diversos aspectos de soluciones cosmológicas obtenidas a partir de teorías de gravedad modificada. Para entender el origen y la importancia de las teorías de gravedad modificada es necesario comentar antes algunos hechos acontecidos durante el siglo XX en el marco de la cosmología. La cosmología como ciencia nació gracias a la Teoría de la Relatividad General de Albert Einstein. Antes de ésta, el espacio no era más que el lugar en el que las estrellas y los planetas residían y el tiempo no era más que algo que iba pasando, siendo espacio y tiempo dos cosas completamente desconectadas y que no se veían afectadas por lo acontecido en el Universo. Sin embargo, la teoría de Einstein derrumbó estas ideas, proponiendo que espacio y tiempo están ligados entre sí y que, además, no son meros espectadores de lo que sucede en el Universo, sino que se ven afectados por su contenido. Fue de esta manera como surgió el concepto de espacio-tiempo, el cual, según Einstein, se curva debido a la presencia de materia y/o energía (ya unificadas en su teoría de la relatividad especial). Las ecuaciones de campo de Einstein son las ecuaciones que permiten a la cosmología ser considerada como una ciencia, y establecen un diálogo entre la forma del Universo y el contenido de materia y energía que en él hay. Las primeras soluciones cosmológicas que se dieron para el Universo eran estáticas, sin embargo éstas se desecharon cuando se verificó que la ley de expansión propuesta por Hubble era cierta. La teoría más aceptada hoy en día para describir el Universo es la Teoría del Big Bang, que predice un universo en expansión que habría empezado tras una gran explosión. Entre los logros de esta teoría se encuentran el estar de acuerdo con la ley de Hubble, haber podido predecir el fondo de radiación cósmica de microondas o el ser capaz de explicar la abundancia relativa de elementos primordiales. Sin embargo, este modelo no se encuentra exento de problemas, ya que hay ciertos aspectos que la teoría no es capaz de explicar, entre ellos se encuentran el problema de la bariogénesis (explicar el proceso que produce la asimetría encontrada entre bariones y antibariones) o los problemas de la planitud y del horizonte. Si bien es cierto que alguno de estos problemas pueden ser subsanados completando la teoría del Big Bang con otras como el modelo inflacionario, se ha demostrado que estos parches también presentan sus propios problemas. Aún así, la teoría del Big Bang está considerada como la mejor descripción que tenemos del Universo. A pesar de los pequeños o grandes problemas que aún quedaban por resolver, parecía que la cosmología estaba destinada a vivir de manera más o menos plácida. Pero esta aparente calma se vio truncada cuando, a finales del siglo XX, dos grupos liderados por Saul Perlmutter y por Adam Riess y Brian Schmidt, respectivamente, descubrieron, a partir de observaciones de supernovas de tipo Ia, que el Universo se encuentra en una fase de expansión acelerada. Esto contrasta con la visión que aporta la teoría del Big Bang, ya que según este modelo el Universo habría surgido de una gran explosión, fruto de la cual se estaría expandiendo; sin embargo, debido a la atracción gravitatoria de la masa contenida en el Universo, dicha expansión debería ir frenándose. Además, el grupo de Perlmutter determinó que, para poder explicar este hecho en el seno de la teoría del Big Bang, asumiendo un Universo espacialmente plano, la materia ordinaria y la materia oscura aportarían un 28% del total del contenido del Universo, mientras que el 72% restante debería atribuirse a un tipo de energía exótica denominada energía oscura y que ejercería una fuerza repulsiva. El descubrimiento de la expansión acelerada del Universo fue el origen del surgimiento de un gran número de teorías cuyo objetivo era darle una explicación. La más aceptada actualmente es la teoría ¿-Cold-Dark-Matter (¿CDM) la cual propone que la energía oscura no es más que una constante cosmológica que daría cuenta de la energía de vacío del Universo. Otras teorías muy populares entre los cosmólogos para dar una explicación a la energía oscura son las teorías escalar-tensor, en las cuales la aceleración se consigue mediante la introducción de un campo escalar en el lagrangiano de la teoría, de manera similar a como el inflatón consigue la aceleración en el periodo de inflación. Básicamente, las teorías comentadas hasta ahora se basan en la introducción de algún tipo de materia o energía exótica en las ecuaciones de campo de Einstein para conseguir la aceleración deseada en el Universo. Sin embargo, ésta no es la única forma de conseguir el resultado deseado. Otra manera es suponer que las ecuaciones de Einstein son válidas hasta un cierto límite, pero han de ser modificadas más allá de este. De esta forma la aceleración en la expansión no estaría causada por un tipo de materia/energía exótica, sino que sería consecuencia de las nuevas ecuaciones. A este tipo de teorías es a las que se conoce como teorías de gravedad modificada. Entre los modelos que proponen modificar las ecuaciones de Einstein, para intentar dar una explicación a la actual aceleración en la expansión del Universo, se encuentran las teorías de gravedad modificada f(R). Estas teorías se basan en la sustitución de la curvatura escalar, R, en la acción de Einstein-Hilbert por una función genérica de la misma, f(R). Esta modificación, que a priori puede no parecer especialmente traumática, se traduce finalmente en que las ecuaciones de campo derivadas de la nueva acción sean ecuaciones diferenciales no lineales de cuarto orden, en lugar de ser de segundo orden como es el caso de las ecuaciones de campo de Einstein. Una parte muy importante, si bien no es la única, de los esfuerzos realizados para llevar a cabo este trabajo de tesis se basa en el estudio de diversos aspectos de diferentes teorías de gravedad modificada f(R). Uno de los bloques fundamentales de la memoria de la tesis es aquél dedicado a la reconstrucción de soluciones cosmológicas a partir de diferentes teorías gravitatorias. El objetivo es determinar si es posible encontrar una acción que sea capaz de reproducir una cosmología, dada por su factor de escala o su función de Hubble, y, en caso afirmativo, determinar la forma de dicha acción. Esta labor se ha llevado a cabo para teorías de gravedad modificada f(R) mediante el uso de dos esquemas de reconstrucción distintos, uno basado en el uso de un campo escalar y otro en el uso de las ecuaciones de campo obtenidas a partir de la acción de la teoría f(R). En el capítulo 2 se presentarán estos esquemas de reconstrucción y se analizarán los resultados obtenidos mediante el uso de ambos para una misma cosmología dada. Posteriormente, en el capítulo 3, se extenderá el uso de estos programas de reconstrucción a modelos cosmológicos acoplados de manera mínima a campos de Yang-Mills, estudiando de nuevo lo que ocurre con las soluciones obtenidas a partir de ambos métodos para una misma cosmología. Además, se llevará a cabo el desarrollo de un programa de reconstrucción para teorías de Yang-Mills acopladas de manera no-mínima a gravedad. Para terminar con el bloque dedicado a la reconstrucción de soluciones cosmológicas, se estudiará el caso de universos cíclicos en el seno de teorías de gravedad de Horava¿Lifshitz modificada. La gravedad de Horava-Lifshitz es una teoría renormalizable, propuesta por Horava, basada en la introducción de una anisotropía entre las cordenadas espaciales y la temporal, con la cual se rompe la invariancia bajo difeomorfismos de la Relatividad General. En el capítulo 4, se hará uso de los métodos de reconstrucción estudiados anteriormente para reconstruir un universo cíclico en el seno de teorías de gravedad de Horava¿Lifshitz modificada, dichas teorías se obtienen mediante una generalización del modelo de Horava-Lifshitz, de manera similar a como se obtienen las teorías f(R) a partir de la acción de Einstein-Hilbert. El estudio de la historia cósmica, y del crecimiento de las perturbaciones de densidad de materia, para diversos modelos f(R) viables constituye otra de las partes fundamentales de esta memoria de tesis. Debido a la arbitrariedad de la función f(R), existen infinitas teorías de este tipo, tantas como funciones que se puedan proponer; sin embargo, no todas ellas son viables, para ello han de cumplir con una serie de condiciones, como pueden ser pasar los tests de Sistema Solar y tener un acoplo gravitacional efectivo positivo. En el capítulo 5 se hará un estudio de la historia cósmica para dos modelos viables. Se analizarán numéricamente las oscilaciones de alta frecuencia de energía oscura producidas durante la época de dominación de materia, las cuales pueden producir algunas divergencias. Es por ello que se propondrán unos términos correctivos para los modelos que ayudarán a estabilizar estas oscilaciones sin hacer perder la viabilidad a los modelos. Para estas nuevas teorías se hará un estudio de la evolución que tendrían en el futuro y, además, se analizará de manera exhaustiva la historia de crecimiento de las perturbaciones de densidad de materia. Para llevar a cabo esta última tarea se determinará el índice de crecimiento para ambos modelos según tres parametrizaciones distintas. En la segunda parte del capítulo 5 se realizará un análisis de la época inflacionaria para dos modelos exponenciales. Para terminar con este bloque, en el capítulo 6, se estudiará el crecimiento de las perturbaciones de densidad de materia, de manera similar a como se hizo en el capítulo 5, para dos nuevos modelos f(R) viables. Un tercer bloque, que consta de dos capítulos, se dedica al estudio de otros aspectos importantes para las teorías gravitatorias, como es el caso del problema de la aparición de singularidades y el estudio del límite de campo débil en teorías f(R,G), siendo G el invariante de curvatura de Gauss-Bonnet. El caso de la existencia de singularidades futuras en el seno de teorías de gravedad modificada y de energía oscura es tratado en el capítulo 7, en el cual también se dará una clasificación de las mismas dependiendo de la magnitud causante de la divergencia. Si bien es cierto que, para tratar de manera rigurosa el tema de las singularidades, es necesaria una teoría cuántica de la gravedad, de la que aún hoy carecemos, también es importante intentar encontrar escenarios naturales a nivel clásico o semiclásico que sean capaces de curar la aparición de estas singularidades. En el capítulo 7 se propondrá una posible cura para este problema, la cual está basada en la adición de un término R^2 en el Lagrangiano de la teoría. Tras este análisis del problema de la aparición de singularidades en el seno de distintas teorías gravitatorias, en el capítulo 8 se afronta el estudio del límite de campo débil para las teorías de gravedad modificada f(R,G). Hasta finales del siglo XX, la Relatividad General de Einstein se había mostrado como la teoría gravitatoria más fiable, debido a la excelente concordancia entre sus predicciones y los datos observacionales que se tenían en ese momento. Sin embargo, el descubrimiento del actual estado de aceleración, en el que se ve inmersa la expansión del Universo, abrió una grieta en la teoría gravitatoria de Einstein, poniendo en duda su validez a grandes escalas y en regímenes de altas energías. Aún así, los excelentes resultados a cortas escalas, como a nivel de sistema solar, de la Relatividad General hacen que el análisis del límite de campo débil de cualquier teoría gravitatoria sea muy relevante, ya que éstas deberían ser capaces de reproducir los resultados obtenidos por la Relatividad General para pequeñas escalas. De esta manera, el estudio del límite de campo débil puede ser usado para desechar o seguir teniendo en consideranción una teoría gravitatoria. En el capítulo 8, se calcularán los límites Newtoniano, post-Newtoniano y post-post-Newtoniano de las teorías f(R,G); además, el límite Newtoniano se resolverá a partir de funciones de Green. Para finalizar con el capítulo se presentarán los límites Newtoniano, post-Newtoniano y post-post -Newtoniano para dos casos especiales, las teorías f(R) y f(G).} La memoria de la tesis finaliza con un bloque dedicado a las conclusiones generales obtenidas y a las cuestiones que quedan abiertas para un trabajo futuro.

This thesis concerns a range of aspects of theoretical physics. It is composed of two parts. In the first part we motivate our line of research, and introduce and discuss the relevant concepts. In the second part, four research papers are collected. The first paper deals with a possible extension of general relativity, namely the recently discovered classically consistent bimetric theory. In this paper we study the behavior of perturbations of the metric(s) around cosmologically viable background solutions. In the second paper, we explore possibilities for particle physics with low-scale supersymmetry. In particular we consider the addition of supersymmetric higher-dimensional operators to the minimal supersymmetric standard model, and study collider phenomenology in this class of models. The third paper deals with a possible extension of the notion of Lie algebras within category theory. Considering Lie algebras as objects in additive symmetric ribbon categories we define the proper Killing form morphism and explore its role towards a structure theory of Lie algebras in this setting. Finally, the last paper is concerned with the computation of string amplitudes in four dimensional models with reduced supersymmetry. In particular, we develop general techniques to compute amplitudes involving gauge bosons and gravitons and explicitly compute the corresponding three- and four-point functions. On the one hand, these results can be used to extract important pieces of the effective actions that string theory dictates, on the other they can be used as a tool to compute the corresponding field theory amplitudes.
Over the last twenty years there have been spectacular observations and experimental achievements in fundamental physics. Nevertheless all the physical phenomena observed so far can still be explained in terms of two old models, namely the Standard Model of particle physics and the ΛCDM cosmological model. These models are based on profoundly different theories, quantum field theory and the general theory of relativity. There are many reasons to believe that the SM and the ΛCDM are effective models, that is they are valid at the energy scales probed so far but need to be extended and generalized to account of phenomena at higher energies. There are several proposals to extend these models and one promising theory that unifies all the fundamental interactions of nature: string theory. With the research documented in this thesis we contribute with four tiny drops to the filling of the fundamental physics research pot. When the pot will be saturated, the next fundamental discovery will take place.

In questa tesi studiamo un'estensione con un termine di interazione cubica di tipo Galileone della lagrangiana dei più semplici modelli scalari-tensoriali, come gravità indotta (IG) e il modello Jordan-Brans-Dicke esteso con un potenziale (eJBD). Ne analizziamo gli effetti cosmologici sia a livello di background che di perturbazioni lineari. Il lavoro si suddivide in una parte analitica ed una numerica: nella parte analitica vengono ricavate le equazioni del moto del modello sia a livello omogeneo che per le perturbazioni lineari e si ottiene una classe di soluzioni analitiche in assenza di materia. La parte numerica, che ha richiesto l'implementazione delle equazioni della teoria in un codice Einstein-Boltzmann dedicato, ci ha permesso di studiare più nel dettaglio l'evoluzione della cosmologia omogenea e fare predizioni sulle anisotropie dello spettro di potenza angolare della radiazione cosmica di fondo (CMB) e dello spettro di potenza della materia, confrontando tali risultati con quelli ottenuti in IG e nel modello cosmologico standard ΛCDM.

This thesis attempts to test several frameworks of non-Newtonian gravity in the context of galaxies and galaxy clusters. The theory most extensively discussed was that of Modified Newtonian Dynamics (MOND) with Galileon gravity, Emergent Gravity (EG) and Modified Gravity (MOG) mentioned to a lesser extent. Specifically, the main focus of this thesis was to determine whether MOND and MOND-like theories were compatible with galaxy cluster data, without the need to include cold dark matter. To do this, the paradigms of Extended MOND (EMOND), Generalised MOND (GMOND) and superfluid dark matter were investigated. The theories were outlined and applied to galaxy cluster data. The main findings of this were that EMOND and GMOND had some success with explaining galaxy cluster mass profiles, without requiring an additional dark matter component. The superfluid paradigm also enjoyed some success in galaxy clusters, which was expected as it behaves in a similar manner to the standard cold dark matter paradigm in cluster environments. However, the superfluid paradigm may have issues in the very centre of galaxy clusters due to the theory predicting constant density cores, whereas the cold dark matter paradigm predicts density cores which are cuspier. The EMOND paradigm was also tested against ultra-diffuse galaxy (UDGs) data as they appear in cluster environments, where EMOND becomes important. It was found that EMOND can reproduce the inferred mass of the UDGs, assuming they lie on the fundamental manifold (FM). The validity of the assumptions used to model the UDGs are discussed in the text. A two-body problem was also conducted in the Galileon gravity framework. The amount of additional gravitational force, compared to Newtonian was determined for a small galaxy at the edge of a galaxy cluster.

Lovelock and Horndeski theories are natural generalisations of Einstein’s theory of General Relativity. They find applications in Astrophysics, Cosmology and String Theory. This dissertation discusses some issues regarding the mathematical consistency of these theories. In the first part of the thesis we study the Shapiro time delay for gravitons in spherically symmetric spacetimes in Einstein–Gauss–Bonnet gravity (a Lovelock theory). In Lovelock theories, gravitons can propagate faster or slower than light. We show that, thanks to this property, it is possible for them to experience a negative time delay. It was recently argued that this feature could be employed to construct closed causal curves, implying that the theory should be discarded as causally pathological. We show that this construction is unphysical, for it cannot be realised as the evolution of sensible initial data. The second part investigates the local well-posedness of the initial value problem for Lovelock and Horndeski theories. For the initial value problem to be well-posed it is necessary that the equations of motion be strongly hyperbolic. It is known that when the background fields are large, even weak hyperbolicity may fail. Hence, we consider the weak field regime, in which these equations can be considered as small perturbations of the Einstein equations. We prove that both Lovelock and Horndeski theories are weakly hyperbolic in a generic weak field background in harmonic and generalised harmonic gauge, respectively. We show that Lovelock theories fail to be strongly hyperbolic in this setting. We also prove that the most general Horndeski theory which is strongly hyperbolic is simply a “k-essence” theory coupled to Einstein gravity and that any more general theory would necessarily fail to be so. Our results imply that the standard methods used to prove the well-posedness of the initial value problem for the Einstein equations cannot be extended to Lovelock or Horndeski theories. This raises the possibility that these theories may not admit a well-posed initial value problem even for weak fields and hence might not constitute a valid alternative to General Relativity.

In this thesis a set of recently proposed multigravity theories is analysed. In the special case of bimetric gravity, the theory has been conclusively shown to be ghost-free. On the other hand, for multigravity theories in general, the ghost-issue has not been settled conclusively. Motivated by this fact, the main object of this thesis is to clarify what has been proven so far and what issues that still needs to be addressed. We also provide new calculations and results pointing in the direction that the multigravity theories must be restricted to a set of bimetric Hassan-Rosen couplings in a tree-type structure in order to be consistent. In particular, we prove that for a multivielbein theory of  interacting vielbeins, the Lorentz equations of motion is a set of  Deser-van Nieuwenhuizen conditions if and only if the theory consists of bimetric Hassan-Rosen couplings in a tree-type structure.

Which tensor fields G on a smooth manifold M can serve as a spacetime structure? In the first part of this thesis, it is found that only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry predictive, interpretable and quantizable matter dynamics. The obvious dependence of this characterization of admissible tensorial spacetime geometries on specific matter is not a weakness, but rather presents an insight: it was Maxwell theory that justified Einstein to promote Lorentzian manifolds to the status of a spacetime geometry. Any matter that does not mimick the structure of Maxwell theory, will force us to choose another geometry on which the matter dynamics of interest are predictive, interpretable and quantizable. These three physical conditions on matter impose three corresponding algebraic conditions on the totally symmetric contravariant coefficient tensor field P that determines the principal symbol of the matter field equations in terms of the geometric tensor G: the tensor field P must be hyperbolic, time-orientable and energy-distinguishing. Remarkably, these physically necessary conditions on the geometry are mathematically already sufficient to realize all kinematical constructions familiar from Lorentzian geometry, for precisely the same structural reasons. This we were able to show employing a subtle interplay of convex analysis, the theory of partial differential equations and real algebraic geometry. In the second part of this thesis, we then explore general properties of any hyperbolic, time-orientable and energy-distinguishing tensorial geometry. Physically most important are the construction of freely falling non-rotating laboratories, the appearance of admissible modified dispersion relations to particular observers, and the identification of a mechanism that explains why massive particles that are faster than some massless particles can radiate off energy until they are slower than all massless particles in any hyperbolic, time-orientable and energy-distinguishing geometry. In the third part of the thesis, we explore how tensorial spacetime geometries fare when one wants to quantize particles and fields on them. This study is motivated, in part, in order to provide the tools to calculate the rate at which superluminal particles radiate off energy to become infraluminal, as explained above. Remarkably, it is again the three geometric conditions of hyperbolicity, time-orientability and energy-distinguishability that allow the quantization of general linear electrodynamics on an area metric spacetime and the quantization of massive point particles obeying any admissible dispersion relation. We explore the issue of field equations of all possible derivative order in rather systematic fashion, and prove a practically most useful theorem that determines Dirac algebras allowing the reduction of derivative orders. The final part of the thesis presents the sketch of a truly remarkable result that was obtained building on the work of the present thesis. Particularly based on the subtle duality maps between momenta and velocities in general tensorial spacetimes, it could be shown that gravitational dynamics for hyperbolic, time-orientable and energy distinguishable geometries need not be postulated, but the formidable physical problem of their construction can be reduced to a mere mathematical task: the solution of a system of homogeneous linear partial differential equations. This far-reaching physical result on modified gravity theories is a direct, but difficult to derive, outcome of the findings in the present thesis. Throughout the thesis, the abstract theory is illustrated through instructive examples.
Welche Tensorfelder G auf einer glatten Mannigfaltigkeit M können eine Raumzeit-Geometrie beschreiben? Im ersten Teil dieser Dissertation wird es gezeigt, dass nur stark eingeschränkte Klassen von Tensorfeldern eine Raumzeit-Geometrie darstellen können, nämlich Tensorfelder, die eine prädiktive, interpretierbare und quantisierbare Dynamik für Materiefelder ermöglichen. Die offensichtliche Abhängigkeit dieser Charakterisierung erlaubter tensorieller Raumzeiten von einer spezifischen Materiefelder-Dynamik ist keine Schwäche der Theorie, sondern ist letztlich genau das Prinzip, das die üblicherweise betrachteten Lorentzschen Mannigfaltigkeiten auszeichnet: diese stellen die metrische Geometrie dar, welche die Maxwellsche Elektrodynamik prädiktiv, interpretierbar und quantisierbar macht. Materiefeld-Dynamiken, welche die kausale Struktur von Maxwell-Elektrodynamik nicht respektieren, zwingen uns, eine andere Geometrie auszuwählen, auf der die Materiefelder-Dynamik aber immer noch prädiktiv, interpretierbar und quantisierbar sein muss. Diesen drei Voraussetzungen an die Materie entsprechen drei algebraische Voraussetzungen an das total symmetrische kontravariante Tensorfeld P, welches das Prinzipalpolynom der Materiefeldgleichungen (ausgedrückt durch das grundlegende Tensorfeld G) bestimmt: das Tensorfeld P muss hyperbolisch, zeitorientierbar und energie-differenzierend sein. Diese drei notwendigen Bedingungen an die Geometrie genügen, um alle aus der Lorentzschen Geometrie bekannten kinematischen Konstruktionen zu realisieren. Dies zeigen wir im ersten Teil der vorliegenden Arbeit unter Verwendung eines teilweise recht subtilen Wechselspiels zwischen konvexer Analysis, der Theorie partieller Differentialgleichungen und reeller algebraischer Geometrie. Im zweiten Teil dieser Dissertation erforschen wir allgemeine Eigenschaften aller solcher hyperbolischen, zeit-orientierbaren und energie-differenzierenden Geometrien. Physikalisch wichtig sind der Aufbau von frei fallenden und nicht rotierenden Laboratorien, das Auftreten modifizierter Energie-Impuls-Beziehungen und die Identifizierung eines Mechanismus, der erklärt, warum massive Teilchen, die sich schneller als einige masselosse Teilchen bewegen, Energie abstrahlen können, aber nur bis sie sich langsamer als alle masselossen Teilchen bewegen. Im dritten Teil der Dissertation ergründen wir die Quantisierung von Teilchen und Feldern auf tensoriellen Raumzeit-Geometrien, die die obigen physikalischen Bedingungen erfüllen. Eine wichtige Motivation dieser Untersuchung ist es, Techniken zur Berechnung der Zerfallsrate von Teilchen zu berechnen, die sich schneller als langsame masselose Teilchen bewegen. Wir finden, dass es wiederum die drei zuvor im klassischen Kontext identifizierten Voraussetzungen (der Hyperbolizität, Zeit-Orientierbarkeit und Energie-Differenzierbarkeit) sind, welche die Quantisierung allgemeiner linearer Elektrodynamik auf einer flächenmetrischen Raumzeit und die Quantizierung massiver Teilchen, die eine physikalische Energie-Impuls-Beziehung respektieren, erlauben. Wir erkunden auch systematisch, wie man Feldgleichungen aller Ableitungsordnungen generieren kann und beweisen einen Satz, der verallgemeinerte Dirac-Algebren bestimmt und die damit Reduzierung des Ableitungsgrades einer physikalischen Materiefeldgleichung ermöglicht. Der letzte Teil der vorliegenden Schrift skizziert ein bemerkenswertes Ergebnis, das mit den in dieser Dissertation dargestellten Techniken erzielt wurde. Insbesondere aufgrund der hier identifizierten dualen Abbildungen zwischen Teilchenimpulsen und -geschwindigkeiten auf allgemeinen tensoriellen Raumzeiten war es möglich zu zeigen, dass man die Gravitationsdynamik für hyperbolische, zeit-orientierbare und energie-differenzierende Geometrien nicht postulieren muss, sondern dass sich das Problem ihrer Konstruktion auf eine rein mathematische Aufgabe reduziert: die Lösung eines homogenen linearen Differentialgleichungssystems. Dieses weitreichende Ergebnis über modifizierte Gravitationstheorien ist eine direkte (aber schwer herzuleitende) Folgerung der Forschungsergebnisse dieser Dissertation. Die abstrakte Theorie dieser Doktorarbeit wird durch mehrere instruktive Beispiele illustriert.

The aim of this thesis is to study the possible astrophysical and cosmological applications of Extended Theories of Gravity. In particular, Neutron Stars are studied, both on astrophysical and cosmological scale where, at cosmological level, they can assume a macroscopic configuration, i.e. a cosmological probe, which can be represented like a Fermionic condensate. The goal is to provide answers consistent with observational evidences that are not justified by General Relativity.

The cosmological constant is not the only possibility in order to describe the accelerated expansion of the Universe. A different approach is to modify the gravitational sector of the Einstein equations. In scalar-tensor theories the gravitational interaction is affected by both a scalar and a tensor field. The dependence of gravity from the scalar field is obtained through a non-minimal coupling function which multiplies the Ricci scalar in the Lagrangian. In this thesis we consider a specific shape of the coupling function that reduces to the minimal coupling case and to the induced gravity case for specific choices of the parameters. We consider two shapes for the potential: one leads to an effectively massless Klein-Gordon equation while the other is motivated by the fact that it is a viable potential for the chaotic inflation in superconformal theory. For the former we consider also the conformal coupling case, which is the required coupling in order to obtain a conformally invariant theory. We derive the fundamental equation at the background and linear perturbations level and then we recover the initial condition for the perturbations. In order to study the evolution for the background and linear fluctuations within non-minimally coupling we modified the publicly available Einstein-Boltzmann code CLASS. The evolution of the dark energy density parameter and the equation of state are shown. Furthermore we pay attention to the actual value of the post-Newtonian parameters in order to see which choices of the parameters satisfies the Solar System constraints. We present the results obtained for CMB anisotropies, linear matter power spectrum, metric and scalar field perturbations. As for the background we confront them with the ΛCDM model for both the potential considered.

This thesis investigates black holes and gravitational waves in the framework of quadratic gravity. These subjects are introduced by first examining the current state of general relativity and how it is realised. The discussion then addresses the quantitative aspects of black holes, gravitational waves, and quadratic gravity. This is then followed by the exploration of the three main research topics. The first research topic investigates the induced charging of a black hole due to a topological term in quadratic gravity. The second research topic focuses on the approximate analytic non-Schwarzschild black hole solutions in quadratic gravity. Finally, gravitational waves generated by binary systems within quadratic gravity are studied, with a focus on the corrections produced by the massive scalar field and the massive spin-2 field.

L'un des plus grands problèmes ouverts de la cosmologie moderne est l'origine de l'expansion accélérée de l'Univers, découverte en 1998. L'explication théorique la plus simple repose sur l'introduction d'une constante cosmologique Λ. Ce modèle, connu sous le nom de Lambda CDM, est en accord avec les différentes observations liées à l'expansion accélérée. Cependant, il présente des problèmes d'ordre théorique. Par conséquent, plusieurs alternatives, connues collectivement sous le nom de {it modèles d'énergie noire}, ont été proposées pour expliquer cette accélération. Plusieurs d'entre eux restent viables, car leurs {it backgrounds} cosmologiques ne présentent pas de signatures identifiables. Par contre, les effets sur les phénomènes perturbatifs sont plus spécifiques à chacun de ces modèles. Dans cette thèse, nous explorons les caractéristiques particulières de la croissance des perturbations de matière à l'ordre linéaire dans les théories f(R) avec un regard complémentaire sur les modèles chameleon. La paramétrisation du taux de croissance de la matière en termes d'une fonction γ permet d'identifier une signature très spécifique de ces modèles en comparaison avec le modèle Lambda CDM. Une étude supplémentaire a permis de trouver une dépendance en échelle explicite, nommée {it dispersion}, dans la croissance des perturbations. Des observations plus précises pourraient permettre de faire la différence entre ces différents modèles selon la présence de ces caractéristiques
One of the most important open issues in modern cosmology is the origin of the accelerated expansion of the Universe, observed in 1998. The simplest theoretical explanation relies on the introduction of a cosmological constant Λ. This model, known as LambdaCDM, agrees with all the different observations connected to the accelerated expansion. However, it presents some theoretical issues. As a result, several alternatives, known collectively under the name of {it dark energy models}, have been proposed to explain this acceleration. Several among them remain viable, since their cosmological backgrounds do not show any identifiable signature. On the other hand, effects on the perturbative level are more specific to each model. In this thesis, we explore the particular characteristics of the growth of linear matter perturbations in f(R) theories, with a complementary look on chameleon models. The parameterization of the growth rate in terms of a γ function allows us to identify a very specific signature of these models in comparison with the Lambda CDM model. A subsequent study allowed us to find an explicit scale dependance, known as {it dispersion}, in the growth of perturbations. More precise observations could enable us to distinguish between dark energy models according to the presence of this type of feature

General relativity (GR) has stood as the most accurate description of gravity for the last 100 years, weathering a barrage of rigorous tests. However, attempts to derive GR from a more fundamental theory or to capture further physical principles at high energies has led to a vast number of alternative gravity theories. The individual examination of each gravity theory is infeasible and as such a systematic method of examining modified gravity theories is a necessity. Studying generic classes of gravity theories allows for general statements about observables to be made independent of explicit models. Take, for example, those models described by the Horndeski action, the most general class of scalar-tensor theory with at most second-order derivatives in the equations of motion, satisfying theoretical constraints. But these constraints alone are not enough for a given modified gravity model to be physically viable and hence worth studying. In particular, observations place incredibly tight constraints on the size of any deviation in the solar system. Hence, any modified gravity would have to mimic GR in such a situation. To accommodate this requirement, many models invoke screening mechanisms which suppress deviations from GR in regions of high density. But these mechanisms really upon non-linear effects and so studying them in complex models is mathematically complex. To constrain the space of actions of Horndeski type to those which pass solar-system tests, a set of conditions on the four free functions of the Horndeski action are derived which indicate whether a specific model embedded in the action possesses a GR limit. For this purpose, a new and surprisingly simple scaling method is developed, identifying dominant terms in the equations of motion by considering formal limits of the couplings that enter through the new terms in the modified gravity action. Solutions to the dominant terms identify regimes where nonlinear terms dominate and Einstein's field equations are recovered to leading order. Together with an efficient approximation of the scalar field profile, one can determine whether the recovery of Einstein's field equations can be attributed to a genuine screening effect. The parameterised post-Newtonian (PPN) formalism has enabled stringent tests of static weak-field gravity in a theory-independent manner. This is through parameterising common perturbations of the metric found when performing a post-Newtonian expansion. The framework is adapted by introducing an effective gravitational coupling and defining the PPN parameters as functions of position. Screening mechanisms of modified gravity theories can then be incorporated into the PPN framework through further developing the scaling method into a perturbative series. The PPN functions are found through a combination of the scaling method with a post-Newtonian expansion within a screened region. For illustration, we show that both a chameleon and cubic galileon model have a limit where they recover GR. Moreover, we find the effective gravitational constant and all PPN functions for these two theories in the screened limit. To examine how the adapted formalism compares to solar-system tests, we also analyse the Shapiro time delay effect for these two models and find no deviations from GR insofar as the signal path and the perturbing mass reside in a screened region of space. As such, tests based upon the path light rays such as those done by the Cassini mission do not constrain these theories. Finally, gravitational waves have opened up a new regime where gravity can be tested. To this end, we examine how the generation of gravitational waves are affected by theories of gravity with screening to second post-Newtonian (PN) order beyond the quadrupole. This is done for a model of gravity where the black hole binary lies in a screened region, while the space between the binary's neighbourhood and the detector is described by Brans-Dicke theory. We find deviations at both 1.5 and 2 PN order. Deviations of this size can be measured by the Advanced LIGO gravitational wave detector highlighting that our calculation may allow for constraints to be placed on these theories. We model idealised data from the black hole merger signal GW150914 and perform a best fit analysis. The most likely value for the un-screened Brans-Dicke parameter is found to be ω = -1:42, implying on large scales gravity is very modified, incompatible with cosmological results.

This Thesis is devoted to the study of phenomenologically viable gravitational theories, in order to address the most pressing open issues both at very small and very large energy scales. Lovelock’s theorem singles out General Relativity as the only theory with secondorder field equations for the metric tensor. So, two possible ways to circumvent it and modify the gravitational sector are taken into account. The first route consists in giving up diffeomorphism invariance, which generically leads to extra propagating degrees of freedom. In this framework Horava gravity is discussed, presenting two restrictions, called respectively "projectability" and "detailed balance", which are imposed in order to reduce the number of terms in the full theory. We introduce a new version of the theory assuming detailed balance but not projectability, and we show that such theory is dynamically consistent as both the spin-0 and spin-2 gravitons have a well behaved dynamics at low-energy. Moreover three-dimensional rotating black hole solutions are found and fully studied in the context of Horava gravity, shedding light on its causal structure. A new concept of black hole horizon, dubbed "universal horizon", arises besides the usual event horizon one, since in Lorentz-violating gravity theories there can be modes propagating even at infinite speed. The second route which is considered, consists in adding extra fields to the gravitational action while diffeomorphism invariance is preserved. In this respect we consider the less explored option that such fields are auxiliary fields, so they do not satisfy dynamical equations but can be instead algebraically eliminated. A very general parametrization for these theories is constructed, rendering also possible to put on them very tight, theory-independent constraints. Some insight about the cosmological implications of such theories is also given. Finally in the conclusions we discuss about the future challenges that the aforementioned gravity theories have to face.

The standard Lambda Cold Dark Matter (ΛCDM) model has proven to be extremely powerful in predicting the evolution and formation of the structure we see in the Universe. However, this success comes at the price of accepting that the energy/matter content of the Universe is dominated by two unknown components: dark matter and dark energy. Moreover, in the case of dark matter some tension between simulations and observations exists at galactic scales, while in the case of dark energy long-standing theoretical issues are still unresolved, thus making the investigation of alternative models a powerful and necessary tool to improve the understanding of the Universe dynamics. In this thesis we study a modified gravity model for dark matter, investigating both its theoretical and phenomenological consequences. In particular, we consider a CDM model in which a dark fluid becomes non-minimally coupled to gravity at recent times and investigate and discuss how this modified picture may be able to address some of the issues the CDM paradigm is facing at small scales, while preserving the successes of the model at large scales. On a more formal level we investigate the properties of the Horndeski action under disformal metric transformation, providing the form of the transformations that leaves it invariant. More than a mathematical curiosity, this invariance represents a first step to formalize some recently notices relations between different models of dark energy, which may be seen as equivalent representation of the same fundamental theory.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work we do an investigation of new features of so-called k-defects, which are topological defects with non-canonical kinetic term. Specifically, we study a class of k-defects in models of scalar field theories distinct from standard theory but discribing, case to case, the very same defect structure with the very same energy density as that described by the theory governed by standard Lagrange density. In teories which presents such relationships, distinct models support the same topological structure; why call them of twinlike models. We then build a model of twin theory, which we call ALTW model, and find the relationships between them, including relations between the potentials of both, which, although distinct, they present minima that are connected by the same field solution, for the case of static and stable configurations. The results are ilustrated with several examples. In order to distinguish between theories, we analyze the situation in which the component T11 of the energy-momentum tensor is nonzero, which is equivalent to breaking the pressureless condition required to ensure stability of static solutions. With the same purpose of distinction, we did a study of linear stability of defects and we found that, although representing the same defect structure, case to case, a theory is not a simple reparametrization of the other. We also made an extension of the twin nature between more general models of real scalar field theries and an application to braneworld scenario. We also investigated the behavior twin between standard and tachyonic models in FRW cosmology, where the scalar field evolves over time.
No presente trabalho fazemos uma investigação de novas características dos chamados kdefeitos, que são defeitos topológicos com termo cinético não-canônico. Especificamente, estudamos uma classe de k-defeitos em modelos de teorias de campos escalares distintos da teoria padrão mas que descrevem, caso a caso, o mesmo defeito com a mesma densidade de energia daquele descrito pela teoria governada pela densidade lagrangiana padrão. Em teorias que apresentam tais relações, modelos distintos suportam a mesma estrutura topológica; daí chamá-los de modelos gêmeos. Construímos, então, um modelo de teoria gêmea, que denominamos modelo ALTW, e encontramos as relações existentes entre eles, incluindo as relações entre os potenciais de ambos, que, embora distintos, apresentam mínimos conectados pelo mesmo campo solução, para o caso de configurações estáticas e estáveis. Os resultados são ilustrados com vários exemplos. Com a finalidade de distinguir as teorias, analisamos a situação em que a componente T11 do tensor energia-momento é não-nula, o que é equivalente a quebrar a condição de pressão nula necessária para garantir a estabilidade das soluções estáticas. Com o mesmo objetivo de distinção, fizemos um estudo da estabilidade linear dos defeitos e obtivemos que, embora representem o mesmo defeito, caso a caso, uma teoria não é uma simples reparametrização da outra. Fizemos ainda uma extensão da natureza gêmea entre modelos mais gerais de teorias de campo escalar real e uma aplicação ao cenário de brana. Investigamos também o comportamento gêmeo entre os modelos padrão e taquiônico em cosmologia FRW, onde o campo escalar evolui com o tempo.

The work of this dissertation will study various aspects of the dynamics of compact objects using numerical simulations.We consider BH dynamics within two modified or alternative theories of gravity. Within a family of Einstein-Maxwell-Dilaton-Axion theories, we find that the GW waveforms from binary black hole (BBH) mergers differ from the standard GW waveform prediction of GR for especially large axion values. For more astrophysically realistic (i.e. smaller) values, the differences become negligible and undetectable. Weestablish the existence of a well-posed initial value problem for a second alternative theory fo gravity (quadratic gravity) and demonstrate in spherical symmetry that a linear instability is effectively removed on consideration of the full nonlinear theory.We describe the key components and development of a code for studying BBH mergers for which the mass ratio of the binaries is not close to one. Such intermediate mass ratio inspirals (IMRIs) are much more difficult to simulate and present greater demands on resolution, distributed computing, accuracy and efficiency. To this end, we present a highly-scalable framework that combines a parallel octree-refined adaptive mesh with a wavelet adaptive multiresolution approach. We give results for IMRIs with mass ratios up to 100:1. We study the ejecta from BNS in Newtonian gravity. Using smoothed particle hydrodynamics we develop and present the highly scalable FleCSPH code to simulate such mergers. As part of the ejecta analysis, we consider these mergers and their aftermath as prime candidates for heavy element creation and calculate r-process nucleosynthesis within the post-merger ejecta. Lastly we consider a non-standard, yet increasingly explored, interaction between a BH and a NS that serves as a toy model for primordial black holes (PBH) and their possible role as dark matter candidates. We present results from a study of such systems in which a small BH forms at the center of a NS. Evolving the spherically symmetric system in full GR, we follow the complete dynamics as the small BH consumes the NS from within. Using numerical simulations, we examine the time scale for the NS to collapse into the PBH and show that essentially nothing remains behind. As a result, and in contradiction to other claims in the literature, we conclude that thisis an unlikely site for ejecta and nucleosynthesis, at least in spherical symmetry.

L'intérêt majeur des travaux exposés dans cette thèse est d'explorer la chevelure des trous noirs dans des cadres plus généraux que celui de la Relativité Générale en tenant compte de la présence d'une constante cosmologique, de dimensions supplémentaires, de champs de matière exotiques ou de termes de courbure de rang plus élevé. Ces extensions de la Relativité Générale peuvent s'inscrire dans le cadre de la théorie des cordes. C'est en étudiant des extensions naturelles de la Relativité Générale que nous pouvons aussi mieux comprendre la théorie d'Einstein. Dans un premier temps, nous exposerons la théorie de la Relativité Générale avec notamment les principes sur lesquelles elle s'appuie et nous donnerons les éléments mathématiques dont nous avons besoin pour la suite. Puis, une première extension sera présentée avec l'introduction de dimensions supplémentaires et de champs de p-formes qui constituent la généralisation naturelle de l'interaction électromagnétique. Nous construirons dans ce cadre de nouvelles solutions statiques de trous noirs où les p-formes permettent de modeler la géométrie de l'horizon. Nous exposerons ensuite l'extension la plus générale de la théorie d'Einstein en dimension quelconque qui génère des équations du second ordre en la métrique : la théorie de Lovelock. Nous déterminerons dans ce contexte une large classe de solutions en dimension 6 pour laquelle la théorie se réduit à celle d'Einstein-Gauss-Bonnet avec toujours la présence de p-formes. Enfin, nous étudierons une généralisation de la Relativité Générale en dimension 4 dont la modification est induite par un champ scalaire couplé conformément à la gravitation. Nous exhiberons notamment une nouvelle solution de trou noir avec un horizon plat dans cette théorie en présence de champs axioniques. Pour clore cette thèse, l'aspect thermodynamique de ces théories gravitationnelles sera étudié ; ce qui permettra de déterminer la masse et les charges de ces nouvelles solutions et d'étudier des phénomènes de transitions de phase en présence d'un champ scalaire conforme.

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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Nesta tese exploramos diferentes aspectos de teorias clássicas e quânticas de campos. Na parte clássica, examinamos o fenômeno da birrefringência eletro-magneto-óptica em ele-trodinâmica não-linear no contexto de meios materiais dielétricos não-lineares como uma correção efetiva à teoria linear maxwelliana do eletromagnetismo. Na parte quântica, seguindo o método do heat kernel em teoria quântica de campos sobre espaços curvos, derivamos e estudamos a estrutura das divergências a 1-loop para a ação efetiva de diferentes modelos. Em particular, no ramo do modelo de Yukawa, exibimos duas novas formas de ambiguidades as quais tomam lugar na ação efetiva de campos fermiônicos através do fenômeno da anomalia multiplicativa não-local. Além disso, analisamos a estrutura das divergências ultravioletas a 1-loop para um modelo recentemente proposto de gravitação massiva livre de fantasmas, e mostramos que esse modelo encontra sérias dificuldades no nível quântico.
In this thesis we explore different aspects in classical and quantum field theories. In the classical part, we examine the phenomenon of electro-magneto-optical birefringence in nonlinear electrodynamics in the context of nonlinear dielectric media as an effective correction to the linear Maxwellian theory of electromagnetism. In the quantum part, following the heat kernel method in quantum field theory on curved spaces, we derive and study the structure of the 1-loop divergences for the effective action of different models. In particular, through the Yukawa model, we show two new forms of ambiguities which take place in the effective action of fermionic fields through the phenomenon of nonlocal multiplicative anomaly. Moreover, we analyzed the structure of ultraviolet divergences at 1-loop for a recently proposed ghost-free massive gravity model, and we show that this model meets serious difficulties at the quantum level.

博士
國立清華大學
物理系
101
Firstly, we explore the cosmological evolutions in four viable f(R) gravity models: Exponential, Hu-Sawicki, Starobinsky and Tsujikawa models. We summarize various viability conditions and explicitly demonstrate that the late-time cosmic acceleration following the matter-dominated stage can be realized in these viable models. We also study equation of state for dark energy and confirm that the crossing of the phantom divide from the phantom phase to the non-phantom (quintessence) one can occur and the future crossings of the phantom divide line wDE = −1 are the generic feature. The curvature singularities in viable f(R) gravity models are examined when the background density is dense. These singularities could be eliminated by adding the R2 term in the Lagrangian. Some of cosmological consequences, in particular the sources for the scalar mode of gravitational waves, are discussed. To illustrate the cosmological constraints on f(R), we concentrate on the exponential gravity model. We use the observational data including Supernova Cosmology Project (SCP) Union2 compilation, Two-Degree Field Galaxy Redshift Survey (2dFGRS), Sloan Digital Sky Survey Data Release 7 (SDSS DR7) and Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP7) in our analysis. Secondly, using the “teleparallel” equivalent of General Relativity as the gravitational sector, which is based on torsion instead of curvature, we add a canonical scalar field, allowing for a nonminimal coupling with gravity. Although the minimal case is completely equivalent to standard quintessence, the nonminimal scenario has a richer structure, exhibiting quintessence-like or phantom-like behavior, or experiencing the phantom-divide crossing. The richer structure is manifested in the absence of a conformal transformation to an equivalent minimally-coupled model. Moreover, we propose the simplest model of teleparallel dark energy with purely a non-minimal coupling to gravity but no self-potential, leading to a single model possessing various interesting features: simplicity, self-potential-free, the guaranteed late-time cosmic acceleration driven by the non-minimal coupling to gravity, tracker behavior of the dark energy equation of state at earlier times, a crossing of the phantom divide at a late time, and the existence of a finite-time future singularity. We find the analytic solutions of the dark-energy scalar field respectively in the radiation, matter, and dark energy dominated eras, thereby revealing the above features. We further illustrate possible cosmic evolution patterns and present the observational constraint of this model obtained by numerical analysis and data fitting. Thirdly, we examine the cosmological evolutions of the equation of state for dark energy wDE in the exponential and logarithmic as well as their combination f(T) theories. We show that the crossing of the phantom divide line of wDE = −1 can be realized in the combined f(T) theory even though it cannot be in the exponential or logarithmic f(T) theory. In particular, the crossing is from wDE > −1 to wDE < −1, in the opposite manner from f(R) gravity models. We also demonstrate that this feature is favored by the recent observational data.

We study and constrain the Hu and Sawicki f(R) model using CMB and weak lensing forecasted data. We also use the same data to constrain extended theories of gravity and the subclass of f(R) theories using a general parameterization describing departures from General Relativity. Moreover we study and constrain also a Dark Coupling model where Dark Energy and Dark Matter are coupled toghether.

Tese de mestrado em Astronomia e Astrofísica, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2011
Recentemente, a enorme quantidade de dados observacionais suportando a expansão do universo tardio, propulsionou a cosmologia em particular e a gravitação em geral para a linha da frente da investigação científica. De facto, o problema da origem da chamada energia escura, constitui um dos problemas mais empolgantes da investigação actual, tanto no campo da física fundamental como no da astrofísica. Neste contexto, é de notar o aparecimento de modificações da Relatividade Geral de Einstein especialmente concebido para lidar com este problema, mas que simultaneamente tentam dar resposta a outras inconsistências do modelo padrão da gravidade, como só por exemplo o problema da matéria escura e o da inflação. Destas destacamos, as teorias escalares tensoriais e as teorias f(R) da gravitação. Neste trabalho, consideramos estas modificações mas, focamos em particular a existência de um conjunto de soluções exactas: os wormholes transitáveis. Estes são hipotéticos túneis no espaço-tempo e, são primariamente úteis como “experiências de pensamento” e, como sondagens teóricas dos fundamentos da Relatividade Geral. No entanto, a sua existência como soluções exactas pode ser entendida como um critério de viabilidade de uma dada teoria. Começamos por analisar a possibilidade da existência destes wormholes no contexto das teorias f(R) da gravitação. Concluímos que esta classe particular de modificações da Relatividade Geral, admite de facto a existência destas soluções exactas que se constituem com o túneis hipotéticos no espaço-tempo. No entanto, dada a bem conhecida correspondência entre as teorias f(R) da gravidade e as teorias de Brans-Dicke, apresentamos novas geometrias túneis em vácuo que generalizam as já bem conhecidas soluções apresentadas na literatura.
In recent years, the overwhelming amount of observational data supporting the late-time accelerated expansion of the Universe has thrusted cosmology in particular and gravitation in general to the forefront of scientific research. In fact, the problem of the origin of the so called dark energy, stands as one of the most tantalizing scientific issues of today’s theoretical investigations, both in the field of fundamental physics and in that of astrophysics. In this context, note must be given to the appearance of modifications of Einstein’s General Relativity, especially designed to deal with this problem, although simultaneously addressing other inconsistencies of the standard view of gravity, such as the dark matter problem and inflation. This is the case of the scalar-tensor theories of gravity and the f(R) modified theories of gravity. In this work, we consider these modifications, but focus on the existence of a specific type of exact solution: traversable wormholes. These are hypothetical tunnels in space-time, and are primarily useful as “gedanken-experiments” and as a theoreticians probe of the foundations of general relativity, although their existence as a solution of the field equations may be regarded as a viability condition of the theory. We begin by analyzing the possibility of the existence of these wormholes in f(R) modified theories of gravity. We conclude that this particular class of modifications does indeed posses these hypothetical space-time tunnels as exact solutions. However, given the well known correspondence between f(R) gravity and Brans-Dicke theories, we present new exact vacuum wormhole geometries that generalize the well-known solutions in the literature.

Cosmology is a branch of science which deals with the study of the origin of the u niverse, its evolution and its eventual fate. The modern cosmology is based on the Big Bang theory, where the universe is considered as emerged out of the Big Bang, which occurred about 13.7 billion years ago. The cosmology assumes the homo geneous (no change during linear motion) and isotropic (no change during angular motion) universe, which is justified on the scales of larger than 100 Mpc. These prop erties lead us to make an assumption about the model of the universe, called the Cosmological Principle. This principle is the basis of the Big Bang cosmology. For the evolution of the universe, various models have been proposed by scientists from time to time. Since the development of general relativity, cosmology has changed our perception of the laws of the universe remarkably. The First Three Minutes written by Steven Weinberg and A Brief History of Time by Stephen Hawking are the famous books which create the interest in this subject. The rapid development in observational cosmology witnesses that the universe is expanding with an accelerated rate. Several theories have been proposed to ex plain the accelerated phenomena for past two decades. It has been observed that a large part of the universe has One a mysterious component with negative pressure, so-called dark energy (DE). The most natural and successful candidate of DE is the cosmological constant which was introduced by Albert Einstein to obtain a static uni verse. Some other DE candidates like scalar fields, Chaplygin gas, holographic dark energy, Ricci dark energy, etc. have been proposed to explain the accelerated expan sion of the universe. Recently, it has been studied that the bulk viscosity and matter creation are another alternative candidates to explain the present acceleration of the universe. The motive of this thesis’s work is to explore the effects of bulk viscosity and matter creation in explaining the dark energy phenomena within the framework of a spatial ly homogeneous and isotropic flat Friedmann-Lemaître-Robertson-Walker metric in xi general relativity and its modified theories. We extract the useful information about the bulk viscosity and matter creation by using observational data to fit the model ac cording to the accepted model. Chapter 1 is introductory in nature. Chapters 2 – 6 are based on the research work published in the form of research papers in reputed refereed journals. The last chapter contains the conclusion and future scope of the thesis work. Each chapter begins with a brief outline of the work carried out in that chapter.

The effective field theory approach is powerful in understanding the low energy phenomena without invoking the UV degrees of freedom. We construct a low energy Lagrangian for ordinary fluid systems (in constrast to superfluid), pure from symmetry considerations and EFT principles. The dynamical fields are the Goldstone excitations, associated with spontaneously broken spacetime translations. It is organized as derivatively coupled theory involving multiple scalar fields. This formalism enables us to study fluid's quantum mechanical properties and dissipative effects. Cosmological models can be built by naturally coupling the fluid EFT to gravity. From the EFT point of view, GR is the unique low energy theory for the spin-2 graviton field and any infrared modification corresponds to adding new degrees of freedom. We focus on two popular classes of modified gravity models, --- the chameleon like theories and the Galileon theory, --- and perform a few reliability checks for their qualifications as modified gravity theories. Furthermore, guiled by the EFT spirit, we develop a cosmological model where primordial inflation is driven by a `solid', defined, in a similar manner as the EFT of fluid. The symmetry breaking pattern differs drastically from that of standard inflationary models: time translations are unbroken. This prevents our model from fitting into the standard EFT description of adiabatic perturbations, with crucial consequences for the dynamics of cosmological perturbations, and exhibits various unusual features.