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Inflationary predictions for the power spectrum of the curvature perturbation have been verified to an excellent degree, leaving many models compatible with observations. In this thesis we studied third-order correlations, that might allow one to further distinguish between inflationary models. From all the possible extensions of the standard inflationary model, we chose to study two-field models with canonical kinetic terms and flat field space. The new feature is the presence of the so-called isocurvature perturbation. Its interplay with the adiabatic perturbation outside the horizon gives birth to non-linearities characteristic of multiple-field models. In this context, we established the second-order gauge-invariant form of the adiabatic and isocurvature perturbation and found the third-order action that describes their interactions. Furthermore, we built on and elaborated the long-wavelength formalism in order to acquire an expression for the parameter of non-Gaussianity fNL as a function of the potential of the fields. We next used this formula to study analytically, within the slow-roll hypothesis, general classes of potentials and verified our results numerically for the exact theory. From this study, we deduced general conclusions about the properties of fNL, its magnitude depending on the characteristics of the field trajectory and the isocurvature component, as well as its dependence on the magnitude and relative size of the three momenta of which the three-point correlator is a function.; Les prédictions d'inflation du spectre de puissance de la perturbation de la courbure ont déjà fait l’objet de vérification d’un excellent niveau, permettant à de nombreux modèles de rester compatibles avec les observations. Dans la présente thèse, nous avons étudié les corrélations de troisième ordre qui pourraient permettre de mieux distinguer les différents modèles d'inflation les uns des autres. Parmi toutes les extensions possibles du modèle standard d'inflation, nous avons choisi d'étudier des modèles de deux champs scalaires à termes cinétiques standards et à métrique des champs plat. La nouveauté introduite par ces modèles est la présence de la perturbation d'isocourbure. Son interaction avec la perturbation adiabatique hors de l'horizon produit des non-linéarités caractéristiques des modèles à plusieurs champs scalaires. Dans, ce contexte, nous avons établi la forme de la perturbation adiabatique et de la perturbation d'isocourbure invariant sous transformations de jauge en deuxième ordre. De plus, nous avons trouvé l'action de troisième ordre qui décrit leurs interactions. En outre, nous avons élaboré le formalisme des grandes longueurs d'onde afin d'obtenir une expression pour le paramètre de non-gaussiannité fNL en fonction du potentiel des champs. Nous avons ensuite, utilisé cette formule pour traiter analytiquement - avec l'hypothèse de slow-roll - des classes générales de potentiels et vérifier nos résultats numériquement par la théorie exacte. De là, nous avons pu tirer des conclusions générales concernant les propriétés de fNL, comme par exemple la dépendance de sa magnitude des caractéristiques du trajet des champs et de la perturbation d'isocourbure, ainsi que sa dépendance de la magnitude et de la taille relative des trois impulsions dont le corrélateur à trois points est fonction.

Inflationary predictions for the power spectrum of the curvature perturbation have been verified to an excellent degree, leaving many models compatible with observations. In this thesis we studied third-order correlations, that might allow one to further distinguish between inflationary models. From all the possible extensions of the standard inflationary model, we chose to study two-field models with canonical kinetic terms and flat field space. The new feature is the presence of the so-called isocurvature perturbation. Its interplay with the adiabatic perturbation outside the horizon gives birth to non-linearities characteristic of multiple-field models. In this context, we established the second-order gauge-invariant form of the adiabatic and isocurvature perturbation and found the third-order action that describes their interactions. Furthermore, we built on and elaborated the long-wavelength formalism in order to acquire an expression for the parameter of non-Gaussianity fNL as a function of the potential of the fields. We next used this formula to study analytically, within the slow-roll hypothesis, general classes of potentials and verified our results numerically for the exact theory. From this study, we deduced general conclusions about the properties of fNL, its magnitude depending on the characteristics of the field trajectory and the isocurvature component, as well as its dependence on the magnitude and relative size of the three momenta of which the three-point correlator is a function., Les prédictions d'inflation du spectre de puissance de la perturbation de la courbure ont déjà fait l’objet de vérification d’un excellent niveau, permettant à de nombreux modèles de rester compatibles avec les observations. Dans la présente thèse, nous avons étudié les corrélations de troisième ordre qui pourraient permettre de mieux distinguer les différents modèles d'inflation les uns des autres. Parmi toutes les extensions possibles du modèle standard d'inflation, nous avons choisi d'étudier des modèles de deux champs scalaires à termes cinétiques standards et à métrique des champs plat. La nouveauté introduite par ces modèles est la présence de la perturbation d'isocourbure. Son interaction avec la perturbation adiabatique hors de l'horizon produit des non-linéarités caractéristiques des modèles à plusieurs champs scalaires. Dans, ce contexte, nous avons établi la forme de la perturbation adiabatique et de la perturbation d'isocourbure invariant sous transformations de jauge en deuxième ordre. De plus, nous avons trouvé l'action de troisième ordre qui décrit leurs interactions. En outre, nous avons élaboré le formalisme des grandes longueurs d'onde afin d'obtenir une expression pour le paramètre de non-gaussiannité fNL en fonction du potentiel des champs. Nous avons ensuite, utilisé cette formule pour traiter analytiquement - avec l'hypothèse de slow-roll - des classes générales de potentiels et vérifier nos résultats numériquement par la théorie exacte. De là, nous avons pu tirer des conclusions générales concernant les propriétés de fNL, comme par exemple la dépendance de sa magnitude des caractéristiques du trajet des champs et de la perturbation d'isocourbure, ainsi que sa dépendance de la magnitude et de la taille relative des trois impulsions dont le corrélateur à trois points est fonction.

We use WMAP 9-year and other CMB data to constrain cosmological models where the primordial perturbations have both an adiabatic and a (possibly correlated) neutrino density (NDI), neutrino velocity (NVI), or cold dark matter density (CDI) isocurvature component. For NDI and CDI we use both a phenomenological approach, where primordial perturbations are parametrized in terms of amplitudes at two scales, and a slow-roll two-field inflation approach, where slow-roll parameters are used as primary parameters. For NVI we use only the phenomenological approach, since it is difficult to imagine a connection with inflation. We find that in the NDI and NVI cases larger isocurvature fractions are allowed than in the corresponding models with CDI. For uncorrelated perturbations, the upper limit to the primordial NDI (NVI) fraction is 24% (20%) at k = 0.002 Mpc^{-1} and 28% (16%) at k = 0.01 Mpc^{-1}. For maximally correlated (anticorrelated) perturbations, the upper limit to the NDI fraction is 3.0% (0.9%). The nonadiabatic contribution to the CMB temperature variance can be as large as 10% (-13%) for the NDI (NVI) modes. Bayesian model comparison favors pure adiabatic initial mode over the mixed primordial adiabatic and NDI, NVI, or CDI perturbations. At best, the betting odds for a mixed model (uncorrelated NDI) are 1:3.4 compared to the pure adiabatic model. For the phenomenological generally correlated mixed models the odds are about 1:100, whereas the slow-roll approach leads to 1:13 (NDI) and 1:51 (CDI)., Comment: 17 pages, 11 figures, 5 tables. V2: 3 references added

We investigate the correspondence between a perfect fluid and a scalar field and show a possible way of expressing thermodynamic quantities such as entropy, particle number density, temperature and chemical potential in terms of the scalar field phi and its kinetic term X. We prove a theorem which relates isentropy with purely kinetic Lagrangian. As an application, we study the evolution of the gravitational potential in cosmological perturbation theory., Comment: 18 pages, comments and references added. Section 6 expanded

One of the main problems of Cosmology is to conciliate the initial homogeneity and isotropy of the Universe with the subsequent formation of galaxies. In order to find a solution, the Cosmic Microwave Radiation was deeply investigated and a very small anisotropy was finally detected and indicated as the cause of the structure formation. In the standard cosmological theory it is often demonstrated that the linear perturbations do not evolve in a way able to explain the large scale structure of the today observed Universe. In our paper we want to give a simple counterexample showing that it would be possible the formation of a clustered structure in the Universe without the help of the existence of Dark Matter.

We present the first calculation of the Bayesian evidence for different prototypical single field inflationary scenarios, including representative classes of small field and large field models. This approach allows us to compare inflationary models in a well-defined statistical way and to determine the current "best model of inflation". The calculation is performed numerically by interfacing the inflationary code FieldInf with MultiNest. We find that small field models are currently preferred, while large field models having a self-interacting potential of power p>4 are strongly disfavoured. The class of small field models as a whole has posterior odds of approximately 3:1 when compared with the large field class. The methodology and results presented in this article are an additional step toward the construction of a full numerical pipeline to constrain the physics of the early Universe with astrophysical observations. More accurate data (such as the Planck data) and the techniques introduced here should allow us to identify conclusively the best inflationary model., 12 pages, 2 figures, uses RevTeX. Misprint corrected, references added. Matches published version

We examine the generation of primordial perturbations during an inflationary epoch in generalised theories of gravity when the equations of motion are derived using the Palatini variational principle. Both f(R) and Scalar-Tensor theories are considered and we compare our results with those obtained under the conventional metric formalism. Non-linear generalisations of the action lead to different theories under the two variational choices and we obtain distinct results for scalar and tensor spectral indices and their ratio. We find the following general result; inflation driven solely by f(R) modifications alone do not result in suitable curvature perturbations whilst Scalar-Tensor theories generate nearly scalar invariant curvature perturbations but no tensor modes., Comment: 9 pages

This thesis is comprised primarily of work from three independent papers, written in collaboration with Sean Carroll, Tim Dulaney, and Heywood Tam. The original motivation for the projects undertaken came from revisiting the standard assumption of spatial isotropy during inflation. Each project relates to the spontaneous breaking of Lorentz symmetry---in early Universe cosmology or in the context of effective field theory, in general. Chapter 1 is an introductory chapter that provides context for the thesis. Chapter 2 is an investigation of the stability of theories in which Lorentz invariance is spontaneously broken by fixed-norm vector "aether" fields. It is shown that models with generic kinetic terms are plagued either by ghosts or by tachyons, and are therefore physically unacceptable. Chapter 3 is an investigation of the phenomenological properties of the one low-energy effective theory of spontaneous Lorentz symmetry breaking found in the previous chapter to have a globally bounded Hamiltonian and a perturbatively stable vacuum---the theory in which the Lagrangian takes the form of a sigma model. In chapter 4 cosmological perturbations in a dynamical theory of inflation in which an Abelian gauge field couples directly to the inflaton are examined. The dominant effects of a small, persistent anisotropy on the primordial gravitational wave and curvature perturbation power spectra are found using the "in-in" formalism of perturbation theory. It is found that the primordial power spectra of cosmological perturbations gain significant direction dependence and that the fractional direction dependence of the tensor power spectrum is suppressed in comparison to that of the scalar power spectrum.

The identity of dark matter is one of the key outstanding problems in both particle and astrophysics. In this thesis, I describe a number of complementary searches for particle dark matter. I discuss how the impact of dark matter on stars can constrain its interaction with nuclei, focussing on main sequence stars close to the Galactic Centre, and on the first stars as seen through the upcoming James Webb Space Telescope. The mass and annihilation cross-section of dark matter particles can be probed with searches for gamma rays produced in astronomical targets. Dwarf galaxies and ultracompact, primordially-produced dark matter minihalos turn out to be especially promising in this respect. I illustrate how the results of these searches can be combined with constraints from accelerators and cosmology to produce a single global fit to all available data. Global fits in supersymmetry turn out to be quite technically demanding, even with the simplest predictive models and the addition of complementary data from a bevy of astronomical and terrestrial experiments; I show how genetic algorithms can help in overcoming these challenges. At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 5: Accepted. Paper 6: Submitted.

Durant ma thèse, j'ai étudié le problème de l'accélération de l'Univers du point de vue observationnel et théorique, et ceci dans le but de comprendre l'accélération de l'Univers à partir de l'étude des structures à grande échelle. Deux pistes sont actuellement explorées pour comprendre ce comportement inattendu. La première solution consiste à introduire dans l'Univers une nouvelle forme d'énergie, appelée énergie sombre. La seconde solution implique la modification de la théorie de la Relativité Générale à grande échelle. En particulier, nous avons étudié différents modèles. Je les ai comparés avec les observations et nous avons montré qu'il n'était pas possible de distinguer entre les deux pistes principales en utilisant la théorie des perturbations linéaires.

We propose a model based on a DBI action for the unification of dark matter and dark energy. This is supported by the results of the study of its background behavior at early and late times, and reinforced by the analysis of the evolution of perturbations. We also perform a Bayesian analysis to set observational constraints on the parameters of the model using type Ia SN, CMB shift and BAO data. Finally, to complete the study we investigate its kinematics aspects, such as the effective equation of state parameter, acceleration parameter and transition redshift. Particularizing those parameters for the best fit one appreciates that an effective phantom is preferred., Comment: 11 pages, 8 figures, revtex, new references

The case of a coupling between dark energy and matter (Coupled Quintessence) or gravity (Extended Quintessence) has recently attracted a deep interest and has been widely investigated both in the Einstein and in the Jordan frames (EF, JF), within scalar tensor theories. Focusing on the simplest models proposed so far, in this paper we study the relation existing between the two scenarios, isolating the Weyl scaling which allows to express them in the EF and JF. Moreover, we perform a comparative study of the behavior of linear perturbations in both scenarios, which turn out to behave in a markedly different way. In particular, while the clustering is enhanced in the considered CQ models with respect to the corresponding Quintessence ones where the coupling is absent and to the ordinary cosmologies with a Cosmological Constant and Cold Dark Matter (LCDM), structures in EQ models may grow slower. This is likely to have direct consequences on the inner properties of non-linear structures, like cluster concentration, as well as on the weak lensing shear on large scales. Finally, we specialize our study for interfacing linear dynamics and N-body simulations in these cosmologies, giving a recipe for the corrections to be included in N-body codes in order to take into account the modifications to the expansion rate, growth of structures, and strength of gravity., Comment: 19 pages, 4 figures. References added, minor changes, published in PRD

We calculate power spectra of cosmological perturbations at high accuracy for two classes of inflation models. We classify the models according to the behaviour of the Hubble distance during inflation. Our approximation works if the Hubble distance can be approximated either to be a constant or to grow linearly with cosmic time. Many popular inflationary models can be described in this way, e.g., chaotic inflation with a monomial potential, power-law inflation and inflation at a maximum. Our scheme of approximation does not rely on a slow-roll expansion. Thus we can make accurate predictions for some of the models with large slow-roll parameters., Comment: 13 pages, 1 figure; section on consistency relations of inflation added; accepted by Physics Letters B

We constrain cosmological models where the primordial perturbations have both an adiabatic and a (possibly correlated) cold dark matter (CDM) or baryon isocurvature component. We use both a phenomenological approach, where the primordial power spectra are parametrized with amplitudes and spectral indices, and a slow-roll two-field inflation approach where slow-roll parameters are used as primary parameters. In the phenomenological case, with CMB data, the upper limit to the CDM isocurvature fraction is \alpha, Comment: 30 pages, 18 figures

A covariant and gauge-invariant approach to radiation energy perturbations particularly useful to describe the evolution of cosmological density fluctuations during the recombination era is presented. The radiation is described in the framework of radiation hydrodynamics by a covariant flux-limited diffusion theory. A closed set of gauge-invariant evolution equations for matter and radiation energy density perturbations is given. An explicit gauge-invariant expression for $\frac{\ensuremath{\Delta}T}{T}$ is found.

We compute one-loop corrections to the power spectrum of the curvature perturbation in single-field slow-roll inflation arising from gravitons and inflaton interactions. The quantum corrections due to gravitons to the power spectrum of the inflaton field are computed around the time of horizon crossing and their effect on the curvature perturbation is obtained on superhorizon scales through the delta-N formalism. We point out that one-loop corrections from the tensor modes are of the same magnitude as those coming from scalar self-interactions, therefore they cannot be neglected in a self-consistent calculation., Comment: LateX file; 29 pages; typo corrected; comments added to Sec. 3 and 4. Matches published version in JCAP

The Planck Collaboration acknowledges the support of: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MINECO, JA, and RES (Spain); Tekes, AoF, and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); ERC and PRACE (EU). A description of the Planck Collaboration and a list of its members, indicating which technical or scientific activities they have been involved in, can be found at http://www.cosmos.esa.int/web/planck/ planck-collaboration. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231. Part of this work was undertaken at the STFC DiRAC HPC Facilities at the University of Cambridge, funded by UK BIS National E-infrastructure capital grants. We gratefully acknowledge the IN2P3 Computer Center (http://cc.in2p3.fr) for providing a significant amount of the computing resources and services needed for this work., We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be ns = 0.968 ± 0.006 and tightly constrain its scale dependence to dns/dln k = −0.003 ± 0.007 when combined with the Planck lensing likelihood. When the Planck high-` polarization data are included, the results are consistent and uncertainties are further reduced. The upper bound on the tensor-to-scalar ratio is r0.002 < 0.11 (95% CL). This upper limit is consistent with the B-mode polarization constraint r < 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. These results imply that V(φ) ∝ φ 2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R 2 inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth PR(k) over the range of scales 0.008 Mpc−1, Planck (http://www.esa.int/Planck) is a project of the European Space Agency (ESA) with instruments provided by two scientific consortia funded by ESA member states and led by Principal Investigators from France and Italy, telescope reflectors provided through a collaboration between ESA and a scientific consortium led and funded by Denmark, and additional contributions from NASA (USA).

Realistic models of particle physics include many scalar fields. These fields generically have nonminimal couplings to the Ricci curvature scalar, either as part of a generalized Einstein theory or as necessary counterterms for renormalization in curved background spacetimes. We develop a gauge-invariant formalism for calculating primordial perturbations in models with multiple nonminimally coupled fields. We work in the Jordan frame (in which the nonminimal couplings remain explicit) and identify two distinct sources of entropy perturbations for such models. One set of entropy perturbations arises from interactions among the multiple fields. The second set arises from the presence of nonminimal couplings. Neither of these varieties of entropy perturbations will necessarily be suppressed in the long-wavelength limit, and hence they can amplify the curvature perturbation, $\zeta$, even for modes that have crossed outside the Hubble radius. Models that overproduce long-wavelength entropy perturbations endanger the close fit between predicted inflationary spectra and empirical observations., Comment: 16 pages, no figures. References added to match published version