Littérature scientifique sur le sujet « Cosmology, Primordial non-Gaussianity, Effective Field Theory »

At first glance, the (indirect) measurement of primordial tensor modes by the BICEP2 Collaboration supports an inflationary paradigm for early universe cosmology together with quantum vacuum fluctuations (aka gravitons) as the origin of the spectrum. In this paper, we argue the observed signal may instead be a signature of semiclassical sources of perturbations during inflation. In this scenario, despite a large tensor-to-scalar ratio r ≃ 0.2, it may be possible to write an effective field theory (EFT) of a rolling scalar field without super-Planckian excursions. If the results from BICEP2 withstand further scrutiny, measurements of primordial non-Gaussianity with large scale structure surveys, and direct detection of gravitational waves (GWs) with the new generation of observatories, will be of paramount importance to elucidate the (quantum) origin of structure in the universe.

Abstract We compare and validate COLA (COmoving Lagrangian Acceleration) simulations against existing emulators in the literature, namely Bacco and Euclid Emulator 2. Our analysis focuses on the non-linear response function, i.e., the ratio between the non-linear dark matter power spectrum in a given cosmology with respect to a pre-defined reference cosmology, which is chosen to be the Euclid Emulator 2 reference cosmology in this paper. We vary three cosmological parameters, the total matter density, the amplitude of the primordial scalar perturbations and the spectral index. By comparing the COLA non-linear response function with those computed from each emulator in the redshift range 0 ≤ z ≤ 3, we find that the COLA method is in excellent agreement with the two emulators for scales up to k ∼ 1 h/Mpc as long as the deviations of the matter power spectrum from the reference cosmology are not too large. We validate the implementation of massive neutrinos in our COLA simulations by varying the sum of neutrino masses to three different values, 0.0 eV, 0.058 eV and 0.15 eV. We show that all three non-linear prescriptions used in this work agree at the 1% level at k ≤ 1 h/Mpc. We then introduce the Effective Field Theory of Dark Energy in our COLA simulations using the N-body gauge method. We consider two different modified gravity models in which the growth of structure is enhanced or suppressed at small scales, and show that the response function with respect to the change of modified gravity parameters depends weakly on cosmological parameters in these models.

In this work, we study the impact of quantum entanglement on the two-point correlation function and the associated primordial power spectrum of mean square vacuum fluctuation in a bipartite quantum field theoretic system. The field theory that we consider is the effective theory of axion field arising from Type IIB string theory compacted to four dimensions. We compute the expression for the power spectrum of vacuum fluctuation in three different approaches, namely (1) field operator expansion (FOE) technique with the quantum entangled state, (2) reduced density matrix (RDM) formalism with mixed quantum state and (3) the method of non-entangled state (NES). For a massless axion field, in all three formalisms, we reproduce, at the leading order, the exact scale invariant power spectrum which is well known in the literature. We observe that due to quantum entanglement, the sub-leading terms for these thee formalisms are different. Thus, such correction terms break the degeneracy among the analysis of the FOE, RDM and NES formalisms in the super-horizon limit. On the other hand, for massive axion field we get a slight deviation from scale invariance and exactly quantify the spectral tilt of the power spectrum in small scales. Apart from that, for massless and massive axion field, we find distinguishable features of the power spectrum for the FOE, RDM, and NES on the large scales, which is the result of quantum entanglement. We also find that such large-scale effects are comparable to or greater than the curvature radius of the de Sitter space. Most importantly, in near future if experiments probe for early universe phenomena, one can detect such small quantum effects. In such a scenario, it is possible to test the implications of quantum entanglement in primordial cosmology.

Abstract We calculate one-loop correction to the two-point functions of curvature perturbation in single-field inflation generated by cubic self-interaction. Incorporating the observed red-tilted spectrum of curvature perturbation, the relevant one-loop correction takes a finite value and inversely proportional to the spectral tilt. Requiring one-loop correction to be much smaller than the tree-level contribution leads to an upper bound on primordial non-Gaussianity. While observationally allowed region of non-Gaussian parameter space is found to be entirely included by the region, where one-loop correction is smaller than the tree-level contribution, an appreciably large region has one-loop correction larger than 1% or even 10% of the latter. If future observations conclude non-Gaussianity falls in such a region, then it would be important to incorporate higher-order corrections to the spectrum in order to achieve precise cosmology. In some extreme cases, where one-loop correction has a comparable magnitude to the tree-level contribution, it might indicate breakdown of the cosmological perturbation theory in the context of single-field inflation.

AbstractIn the context of Effective Field Theory, the Hilbert space of states increases in an expanding universe. Hence, the time evolution cannot be unitary. The formation of structure is usually studied using effective field theory techniques. We study the constraints on effective field theory analyses of early universe models which come from demanding that the factor of the space of states corresponding to length scales where the primordial fluctuations are manifest does not suffer from the unitarity problem. For bouncing and emergent cosmologies, no constraints arise provided that the energy scale of the bounce or emergent phases is smaller than the ultraviolet (UV) cutoff scale. On the other hand, in the case of the inflationary scenario, non-trivial upper bounds on the energy scale of inflation arise.

AbstractRecently proposed Swampland Criteria (SC) and Trans-Planckian Censorship Conjecture (TCC) question the theoretical consistency of inflationary cosmology. While SC can be in tension with the recent observational bound on tensor-to-scalar ratio which is a consequence of single field consistency relation, the requirement of TCC translates to the fact that inflation can not produce a detectable signal for stochastic gravitational wave, raising a question on future prospects of detection of Primordial Gravitational Waves (PGW). But the constraint can be relaxed significantly by considering Non Bunch Davies (NBD) initial states, that in turn brings back the observational relevance of PGW via its 2-point function. Also with NBD states the tension between SC and observational bound on tensor-to-scalar ratio vanishes. Focusing on these theoretical importance of NBD states, in this article we develop consistent 3-point statistics with tensor modes for all possible correlators (auto and mixed) for NBD initial states in a generic, model independent framework of Effective Field Theory of inflation and analyze the properties of the correlators in the light of TCC. We also construct the templates of the corresponding nonlinearity parameters $$f_{NL}$$ f NL for different shapes of relevance and investigate if any of the 3-point correlators could be of interest for future CMB missions. Our analysis reveals that the prospects of detecting the tensor auto correlator are almost nil whereas the mixed correlators might be relevant for future CMB missions.

Abstract We study primordial non-gaussianity in supersolid inflation. The dynamics of supersolid is formulated in terms of an effective field theory based on four scalar fields with a shift symmetric action minimally coupled with gravity. In the scalar sector, there are two phonon-like excitations with a kinetic mixing stemming from the completely spontaneous breaking of diffeomorphism. In a squeezed configuration, fNL of scalar perturbations is angle dependent and not proportional to slow-roll parameters showing a blunt violation of the Maldacena consistency relation. Contrary to solid inflation, the violation persists even after an angular average and generically the amount of non-gaussianity is significant. During inflation, non-gaussianity in the TSS and TTS sector is enhanced in the same region of the parameters space where the secondary production of gravitational waves is sizeable enough to enter in the sensitivity region of LISA, while the scalar fNL is still within the current experimental limits.

Abstract Primordial non-Gaussianity can source μ-distortion anisotropies that are correlated with the large-scale temperature and polarization signals of the cosmic microwave background (CMB). A measurement of μT and μE correlations can therefore be used to constrain it on wavelengths of perturbations not directly probed by the standard CMB anisotropies. We carry out a first rigorous search for μ-distortion anisotropies with Planck data, applying the well-tested constrained ILC component-separation method combined with the needlet framework. We correlate the reconstructed μ map with the CMB anisotropies to derive constraints on the amplitude fNL of the local form bispectrum, specifically on the squeezed configurations with effective wavenumbers ks ≃ 740 Mpc−1 and kL ≃ 0.05 Mpc−1, improving previously estimated constraints by more than an order of magnitude. This enhancement is owing to the fact that we are able to use the full multipole information by carefully controlling biases and systematic effects in the analysis. We also for the first time incorporate constraints from measurements of μE correlations, which further tighten the limits. A combination of the derived Planck μT and μE power spectra yields |fNL| ≲ 6800 (95 per cent c.l.) on this highly squeezed bispectrum. This is only ≃ 3 times weaker than the anticipated constraint from Litebird. Furthermore we show that a combination of Litebird with Planck can improve the expected future constraint by $\simeq 20{{\%}}$. These limits can be used to constrain multi-field inflation models and primordial black hole formation scenarios, thus providing a promising novel avenue forward in CMB cosmology.

The Cosmic Microwave Background (CMB) is for nowadays cosmology what colliders are for Particle Physics. It has been an invaluable help to build what is now known as the Standard Model of Cosmology and shape our knowledge about Inflation and the formation of cosmic structures. More recently, the measurements of anisotropies in the temperature and polarization of the CMB are perfectly compatible with a Universe that has undergone an inflationary phase of exponential expansion, where quantum perturbations were stretched on cosmological scales and evolved into the Large Scale Structure (LSS) that we see today. In particular, any high-energy physics model which aims to explain the first stages of the evolution of the Universe, must face the bounds that CMB observations has put and that seem to favor the simplest realization of inflation, where a single slowly-rolling scalar field drives the expansion of the Universe and sources adiabatic perturbations. Our understanding of inflation however is far away to be complete. The lack of both a compelling theoretical UV mechanism and a definite exclusion of the many possible allowed effects in the primordial perturbations force us to push theoretical and observational research further on. One of the most intriguing possibility to study observational consequences of inflationary models is non-Gaussianity, as it provides a direct link to the interactions between the fields active during inflation. In this thesis, we will review some of the interesting phenomenology that inflation could be responsible of, with particular attention to non-Gaussianity. In this context, symmetries and effective field theories can play a fundamental role and will be one of the main subjects of this work. The outline is as follows: - In Chapter 1 the basic concepts of inflation will be introduced. The main focus will be on primordial quantum perturbations and their dynamics. - In Chapter 2 we will briefly review the physics of the CMB, the observables related to the physics of inflation and their current measurements. Here basic concepts about primordial non-Gaussianity will be introduced. - In Chapter 3 we give an example of how primordial non-Gaussianity can be produced when going beyond the simplest inflationary scenarios. We show that modification of Einstein gravity during inflation could leave potentially measurable imprints on cosmological observables in the form of non-Gaussian perturbations. This is due to the fact that these modifications appear in the form of an extra field that could have non-trivial interactions with the inflaton. We show it explicitly for the case $R+\alpha R^2$, where nearly scale-invariant non-Gaussianity at the level of $\fnl\sim\mathcal{O}(1-10)$ can be obtained, in a ``quasi-local'' configuration. - Chapter 4 contains a review of the approach of the Effective Field theory of Inflation (EFTI) to cosmological perturbations and of the tools that will be used in the following chapters. - Chapters 5 and 6 are devoted to the study of inflationary models with features in the potential or speed of sound of the inflaton, in the context of the EFTI. This approach allows us to study the effects of features in the power-spectrum and in the bispectrum of curvature perturbations, from a model-independent point of view, by parametrizing the features directly with modified ``slow-roll'' parameters. We can obtain a self-consistent power-spectrum, together with enhanced non-Gaussianity, which grows with a quantity that parametrizes the sharpness of the step. With this treatment it will be straightforward to generalize and include features in other coefficients of the effective action of the inflaton field fluctuations. Our conclusion in this case is that, excluding extrinsic curvature terms, the most interesting effects at the level of the bispectrum could arise from features in the first slow-roll parameter or in the speed of sound. Finally, we find the energy-scale beyond which loop contributions have the same size of the tree-level ones and the perturbative expansion breaks down. Requiring that all the relevant energy scales of the problem are below this cutoff, we derive a strong upper bound on the sharpness of the feature, or equivalently on its characteristic time scale, which is independent on the amplitude of the feature itself. We point out that the sharp features which seem to provide better fits to the CMB power spectrum could already be outside this bound, questioning the consistency of the models that predict them. - In Chapters 7 and 8 we will develop the concepts of full-diffeomorphism breaking in the effective theory of primordial perturbations. During single-field inflation, time-reparameterization invariance is broken by a time-dependent cosmological background. Here we want to explore more general setups where also spatial diffeomorphisms are broken. First, we will consider the possibility that this breaking is given by effective mass terms or by derivative operators for the metric fluctuations in the so-called unitary-gauge Lagrangian. Then we also add operators that break discrete symmetries like parity and time-reversal. We investigate the cosmological consequences of the breaking of spatial diffeomorphisms and discrete symmetries, focussing on operators that affect the power spectrum of fluctuations. We identify the operators for tensor fluctuations that can provide a blue spectrum without violating the null energy condition and operators for scalar fluctuations that can lead to non-conservation of the comoving curvature perturbation on superhorizon scales even in single-clock inflation. Moreover, we find that operators that break discrete symmetries lead to new direction-dependent phases for both scalar and tensor modes. - In Chapter 9 we will investigate further the subject of diffeomorphism breaking. Using the Goldstone bosons associated to the symmetry breakings, we examine the observational consequences for the statistics of the scalar and tensor modes, paying particular attention to interactions and three-point functions. We show that this symmetry breaking pattern can lead to an enhanced amplitude for the squeezed bispectra and to a distinctive angle dependence between their three wavevectors. - Chapter 10 contains final considerations and possible future directions. Appendices A and B review some general aspects related to the quantization of inflationary perturbations and the in-in formalism, used to compute the bispectra presented in the main text. Appendices C and D contain some technical details about time and spatial diffeomorphism breaking. In Appendix E we discuss how the results of Chapter 9 indicate prospects for constraining the level of spatial diffeomorphism breaking during inflation.
Il fondo cosmico di microonde (CMB) è per la cosmologia moderna quello che gli acceleratori sono per la Fisica delle Particelle. È stato un aiuto fondamentale nella costruzione di quello che oggi possiamo definire il Modello Standard della Cosmologia, dell'Inflazione e della formazione delle strutture cosmiche. Le sue attuali, precise misurazioni costituiscono la più forte conferma che l'Universo ha attraversato una fase di espansione esponenziale, in cui perturbazioni quantistiche sono evolute fino a formare la struttura su grande scala che oggi vediamo. In particolare, ogni modello di fisica delle alte energie che punti a spiegare i primi stadi di vita dell'Universo deve confrontarsi con i limiti che le osservazioni del CMB hanno posto, che sembrano favorire la più semplice realizzazione dell'Inflazione: un singolo campo scalare "in lento rotolamento'' (slow-roll) che guida l'espansione dell'Universo e fa da sorgente alle perturbazioni adiabatiche. La nostra comprensione dell'Inflazione tuttavia è ben lontana dall'essere completa. Sia la mancanza di un'alternativa teorica completamente convincente che la totale esclusione di tutti i possibili altri effetti ammessi nelle perturbazioni primordiali continuano a spingere la ricerca teorica e sperimentale. Una delle possibilità più interessanti nello studio delle conseguenze osservative di modelli inflazionari è la non-Gaussianità primordiale, poiché permette un collegamento diretto con la fisica delle interazioni tra i campi attivi durante l'Inflazione. In questa Tesi, analizzeremo parte dell'interessante fenomenologia di cui l'inflazione può essere responsabile, ponendo particolare enfasi alla questione della non-Gaussanità. In questo contesto, simmetrie e teorie di campo efficaci possono giocare ruoli decisivi e saranno uno degli argomenti principali di questo lavoro. L'elaborato si svilupperà come segue: - Nel Capitolo 1 saranno introdotti i concetti base dell'Inflazione, con particolare attenzione alla dinamica delle perturbazioni primordiali. - Nel Capitolo 2 rivedremo velocemente la fisica del CMB, gli osservabili legati alla fisica dell'Inflazione e le loro attuali misure. Qui verranno introdotti i concetti base della non-Gaussianità primordiale. - Nel Capitolo 3 diamo un esempio di come la non-Gaussanità può essere prodotta andando oltre gli scenari inflazionari standard. Mostreremo come una modifica della gravità di Einstein durante l'Inflazione potrebbe aver lasciato impronte potenzialmente misurabili negli osservabili cosmologici sotto forma di non-Gaussianità. Queste modifiche infatti appaiono nella forma di un ulteriore campo, che potrebbe avere interazioni non bananli con l'inflatone. Mostreremo esplicitamente il caso $R+\alpha R^2$, in cui può esser prodotta una non-Gaussianità al livello $\fnl\sim\mathcal{O}(1-10)$ in una configurazione detta quasi-locale. - Il capitolo 4 contiene l'introduzione all'approccio della Teoria Effettiva dell'Inflazio\-ne (EFTI) alle perturbazioni cosmologiche e degli strumenti che saranno utilizzati nei capitoli successivi. - I Capitoli 5 e 6 sono dedicati allo studio dei modelli inflazionari con "features'' nel potenziale o velocità del suono dell'inflatone nel contesto della EFTI. Questo approccio permetto di studiare gli effetti delle features nello spettro di potenza e nel bispettro delle perturbazioni di curvatura da un punto di vista indipendente dal modello, parametrizzando le features direttamente in termini di parametri di ``slow-roll'' modificati. È così possibile ottenere un consistente spettro di potenza, insieme a non-Gaussianità che cresce con la quantità che parametrizza la larghezza della feature. Con questo trattamento sarà immediato generalizzare e includere features anche negli altri coefficienti dell'azione effettiva delle perturbazioni. La conclusione in questo caso è che, escludendo termini di curvatura estrinseca, effetti interessanti nel bispettro possono nascere solo da features nel primo parametro di slow-roll e nella velocità del suono. Infine, discuteremo la scala di energia a cui i contributi a loop alle interazioni sono dello stesso ordine dei contributi tree-level e l'espansione perturbativa smette di funzionare. Richiedendo che tutte le scale di energia rilevanti per il problema studiato siano sotto questo cutoff, deriveremo un forte limite sulla larghezza della feature, o, equivalentemente, sulla sua caratteristica scala temporale, indipendentemente dall'ampiezza della feature stessa. Faremo anche notare come una feature molto stretta, che sembra poter garantire un miglior fit ai dati dello spettro di potenza del CMB, potrebbe essere già oltre questo limit, mettendo in dubbio la consistenza del modello che la predice. - Nei Capitoli 7 e 8 svilupperemo il concetto di rottura completa dei diffeomorfismi nella teoria effettiva delle perturbazioni primordiali. Durante l'inflazione con un singolo campo, l'invarianza per riparametrizzazioni temporali è rotta dal background cosmologico dipendente dal tempo. Qui vogliamo esplorare la situazione più generale in cui anche i diffeomorfismi spaziali sono rotti. Per prima cosa, considereremo la possibilità che questa rottura sia data da termini di massa o operatori derivativi per le perturbazioni della metrica nella cosiddetta Lagrangiana in gauge unitaria. Successivamente aggiungeremo anche operatori che rompono simmetrie discrete, come la parità e l'inversione temporale. Investigheremo le conseguenze cosmologiche di queste rotture, concentrandoci su operatori che hanno effetto sullo spettro delle fluttuazioni. Identificheremo gli operatori che possono produrre uno spettro blu per le perturbazioni tensoriali, senza la violazione della "null energy condition'', e operatori che possono portare alla non conservazione delle perturbazioni comoventi di curvatura su scale oltre l'orizzonte anche in Inflazione "single-clock''. Inoltre, troveremo che gli operatori che rompono simmetrie discrete producono nuove fasi, dipendenti dalla direzione, per le funzioni d'onda sia degli scalari che dei tensori. - Nel Capitolo 9 continueremo a studiare la rottura dei diffeomorfismi. Usando i bosoni di Goldstone associati alla rottura di simmetria, esamineremo le conseguenze osservative sulla statistica dei modi scalari e tensoriali, con particolare enfasi alla struttura delle interazioni e delle funzioni a tre punti. Mostreremo che la rottura di queste simmetrie può portare ad un ampiezza aumentata per il bispettro nel limite ``squeezed'' e a una dipendenza angolare caratteristica tra i tre vettori d'onda. - Il Capitolo 10 contiene considerazioni finali e possibili direzioni future. Le Appendici A e B rivisitano alcuni aspetti generali della quantizzazione delle perturbazioni primordiali e il formalismo in-in, usato per il calcolo dei bispettri presentati nel testo principale. Le Appendici C e D contengono alcuni dettagli tecnici sulla rottura dei diffeomorfismi temporali e spaziali. Nell'Appendice E discutiamo invece come i risultati del Capitolo 9 indicano prospettive per vincolare il livello della rottura di diffeomorfismi spaziali durante l'Inflazione.

The study of primordial non-Gaussianity can be considered one of the best avenues to probe inflation, trying to resolve the large degeneracy among different models still present after analyzing Cosmic Microwave Background data. Indeed, on the one hand, the amount of non-Gaussianity in single-field inflation is very tiny and entirely fixed by the spontaneous breaking of time reparameterization; on the other hand, different symmetry breaking patterns, typical of more exotic theories, lead to quite different predictions. In this context, this Ph.D. thesis aims at analyzing the primordial imprints in two and three-point correlation functions relevant for future Large Scale Structure and gravitational waves detection, whose origins can be traced back to an inflationary phase of the Universe, discerning between single and multi-field models. Regarding single-field inflation, a controversial issue concerns the consistency relation describing the three-point correlation functions of the comoving curvature perturbation in the squeezed limit. The common lore is that the consistency relation, which implies a prediction for local non-Gaussianity with $f_{NL}=5, (n_s-1 )/12$, actually is not physical and can be gauged away by a constant rescaling of coordinates. This cancellation is the direct consequence of a gauge redundancy which becomes effective only if the squeezed long mode $k_L$ is precisely zero. Such a limit is not physically observable, and by taking into account a small but finite $k_L$, the cancellation of $f_{NL}$ does not take place. The same technique is often used in the literature to cancel any local $f_{NL}$ of quantities depending on the comoving curvature, as in matter density perturbations and related $f_{ NL}^{GR}=-5/3$, entering in the halo bias scale dependence. In the second part of this thesis, we study in detail a promising class of models that allows a systematic analysis of symmetric breaking pattern during inflation and the impact on primordial non-Gaussianity. By using an effective field theory description, the elementary excitations of the model can be interpreted as phonons in a supersolid. In supersolid inflation, the single-field consistency relation that relates the 3-point function in the squeezed limit to the square of the power spectrum does not hold in general. The lack of the consistency relation is deeply connected with the explicit violation of the Weinberg theorem hypothesis: ``adiabaticity'' (presence of one scalar degree of freedom) and ``isotropy'' (absence of anisotropic stress tensor on large scales). The first is violated by the particular symmetry breaking pattern that requires two propagating scalar degrees of freedom while the second is a consequence of the solid component. We have shown that one can significantly enhance the production of gravitational waves entering the window of LISA sensibility without affecting non-Gaussianity in the scalar sector constrained by PLANCK results.