Auswahl der wissenschaftlichen Literatur 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.