The timescape cosmology represents a potentially viable alternative to the standard homogeneous and isotropic Friedmann--Lemaître--Robertson--Walker (FLRW) cosmology, without the need for dark energy. This thesis first extends the previous work on the timescape cosmology to include a radiation component in the evolution equations for the timescape cosmology and tests of the timescape model are then performed against the Cosmic Microwave Background (CMB) temperature anisotropies from the Planck satellite. Although average cosmic evolution in the timescape scenario only differs substantially from that of FLRW cosmologies at relatively late epochs when the contribution from the energy density of radiation is negligible, a full solution of the Buchert equations to incorporate radiation is necessary to smoothly match parameters to the epoch of photon decoupling and to obtain constraints from CMB data. Here we have extended the matter-dominated solution found in earlier work to include radiation, providing series solutions at early times and an efficient numerical integration strategy for generating the complete solution. To analyse the spectrum of CMB anisotropies in the timescape cosmology we exploit the fact that the timescape cosmology is extremely close to the standard cosmology at early epochs and adapt existing numerical codes to produce CMB anisotropy spectra. To find a FLRW model that matches as closely as possible the timescape expansion history, we have studied and compared a number of matching methods. We perform Markov Chain Monte Carlo analyses on the timescape model parameter space, and fit CMB multipoles 50 ≤ l ≤ 2500 to the Planck satellite data. Parameter fits include a dressed Hubble constant, H₀ = 61.0 kms ⁻¹Mpc⁻¹ (±1.3% stat)(±8% sys), and a present void volume fraction fᵥ₀ = 0.627 (±2.3% stat)(±13% sys). In the timescape model this value of fᵥ₀ means that the galaxy/wall observer infers an accelerating universe, where the apparent acceleration is due to gravitational energy gradients and clock rate differences rather than some dark energy. We find best fit likelihoods which are comparable to that of the best fit ΛCDM cosmology in the same multipole range.

In this work we have examined different methods of averaging in general relativity and cosmology. We developed the method based on Cartan scalars. We computed the backreaction term for a flat LTB model with a special ansatz for the radial function. We found out that it behaves as a positive cosmological constant. In the next part of this thesis we were interested in averaging inside LRS class II dust model. For this family we averaged all the Einstein equations and the resulting system generalizes the Buchert equations. We numerically worked out two concrete examples where deceleration parameter changes its sign from positive to negative. Powered by TCPDF (www.tcpdf.org)

In this thesis, I study the relativistic effects of matter inhomogeneities on the accelerating expansion of the Universe. The acceleration is often taken to be caused by the presence of an exotic fluid called Dark Energy, or else a non-zero 'cosmological constant' term in the field equations of General Relativity. I consider whether this result could instead be an artefact caused by using an incorrect model to interpret observations. The standard 'concordance' cosmological model assumes the Cosmological Principle, which states that the matter distribution on large scales is homogeneous. One possibility is that correction terms appear in the field equations when small-scale inhomogeneities are smoothed over to produce this homogeneous model. These 'backreaction' effects could affect the dynamics of the spacetime, causing an apparent acceleration. I clarify the relationship between acceleration of the averaged spacetime and acceleration inferred from observable quantities, and show that they are closely related in statistically-homogeneous spacetimes. Another possibility is that the Universe could be inhomogeneous on large scales. If there was a large ‘void’, with us at the centre, the lensing of light by the void could reproduce the observations that imply cosmic acceleration. I show that a popular class of void models, based on spherically-symmetric Lemaitre-Tolman-Bondi spacetimes, are unable to simultaneously fit a selection of observational data, thus effectively ruling-out this possibility. These data include the Kinematic Sunyaev-Zel'dovich (KSZ) effect, which is a distortion/shift of the Cosmic Microwave Background (CMB) frequency spectrum caused by the Compton scattering of photons by hot gas in galaxy clusters. This, and other distortions of the CMB frequency spectrum, are sensitive to the degree of anisotropy in the CMB about a scattering cluster. I suggest tests involving these observables that exploit the strong link between isotropy and homogeneity to (a) distinguish between different causes of a deviation from spatial flatness on the horizon scale, and (b) potentially confirm the Cosmological Principle using observations. Finally, I describe a novel Bayesian CMB component separation method for extracting the Sunyaev-Zel'dovich signal of clusters from CMB sky maps.

<p>The propagation of light beams originating from synthetic ‘Type Ia’ supernovae, through an inhomogeneous universe with simplified dynamics, is simulated using a Monte-Carlo Ray-Tracing method. The accumulated statistical (redshift-magnitude) distribution for these synthetic supernovae observations, which is illustrated in the form of a Hubble diagram, produces a luminosity profile similar to the form predicted for a Dark-Energy dominated universe. Further, the amount of mimicked Dark-Energy is found to increase along with the variance in the matter distribution in the universe, converging at a value of Ω_X ≈ 0.7.</p><p>It can be thus postulated that at least under the assumption of simplified dynamics, it is possible to replicate the observed supernovae data in a universe with inhomogeneous matter distribution. This also implies that it is demonstrably not possible to make a direct correspondence between the observed luminosity and redshift with the distance of a cosmological source and the expansion rate of the universe, respectively, at a particular epoch in an inhomogeneous universe. Such a correspondences feigns an apparent variation in dynamics, which creates the illusion of Dark-Energy.</p>

The propagation of light beams originating from synthetic ‘Type Ia’ supernovae, through an inhomogeneous universe with simplified dynamics, is simulated using a Monte-Carlo Ray-Tracing method. The accumulated statistical (redshift-magnitude) distribution for these synthetic supernovae observations, which is illustrated in the form of a Hubble diagram, produces a luminosity profile similar to the form predicted for a Dark-Energy dominated universe. Further, the amount of mimicked Dark-Energy is found to increase along with the variance in the matter distribution in the universe, converging at a value of ΩX ≈ 0.7. It can be thus postulated that at least under the assumption of simplified dynamics, it is possible to replicate the observed supernovae data in a universe with inhomogeneous matter distribution. This also implies that it is demonstrably not possible to make a direct correspondence between the observed luminosity and redshift with the distance of a cosmological source and the expansion rate of the universe, respectively, at a particular epoch in an inhomogeneous universe. Such a correspondences feigns an apparent variation in dynamics, which creates the illusion of Dark-Energy.

In this work we study inhomogeneous cosmological models. After a brief review of applications of inhomogeneous solutions to Einstein equations in cosmology, we give a short description of the most widely used inhomogeneous cosmological models. In the second chapter we study in detail geometrical prop- erties of the Szekeres spacetime and we are concerned with the interpretation of the metric functions in different types of geometries. In the last chapter we model inhomogeneity in Szekeres spacetime. We derive formula for the density contrast and investigate its behaviour. We also derive conditions for the density extremes that are necessary for avoiding the shell crossing singularity in Szekeres spacetime. 1

Le modèle cosmologique standard possède plusieurs lacunes pour une description pertinente de l’évolution de notre univers et de ses constituants. Tout d’abord, il laisse en suspens l’explication de l’origine de la matière noire et de l’énergie sombre. Ces composants, introduits ad hoc afin de satisfaire aux observations, représentent ensemble environ 95% du contenu en énergie de l’univers. Un second problème concerne l’indépendance d’échelle du modèle : quel que soit l’échelle du système considéré, il est attendu une dynamique et une géométrie identiques. Il est possible de se détourner du modèle standard et de s’intéresser à des cosmologies inhomogènes et à leur évolution moyenne. Selon ce formalisme, les inhomogénéités au sein d’une échelle influencent globalement la dynamique de cette dernière par un effet dit de rétroaction. Cette démarche très riche propose également une explication élégante au problème des constituants sombres : tous deux apparaissent comme une manifestation effective des inhomogénéités de distributions de matière et de géométrie. Cette thèse s’intéresse aux propriétés des modèles inhomogènes moyennés en relativité générale. Nous proposons dans un premier temps de décrire le comportement global des inhomogénéités selon une évolution de Chaplygin, et selon une évolution de Ginzburg-Landau. Nous montrons également l’instabilité gravitationnelle globale des solutions de Friedmann-Lemaître-Robertson-Walker. Cette classe de solutions est connue comme étant localement instable sous l’introduction de perturbations ; ici nous montrons qualitativement qu’elle ne fournit pas, en général, une approximation correcte en tant que fond physique. Nous présentons finalement une nouvelle théorie relativiste perturbative, pour laquelle les inhomogénéités scalaires évoluent autour d’un fond général, et non plus autour d’un fond de Friedmann-Lemaître-Robertson-Walker pré-défini. Cette nouvelle étude étend l’applicabilité des cosmologies inhomogènes, et pourrait éventuellement expliquer la formation des grandes structures sans recours à l’énergie noire / The standard cosmological model possesses some shortcomings for a relevent description of our universe and its constituents. First, it leaves in suspense the explanation of the origin of dark matter and dark energy. These components, introduced ad hoc in order to fit the observations, represent about 95% of the total energy. A second issue concerns the scale-independence of the model: whatever the scale of the considered system, it is expected identical dynamics and geometry. It is advisable to abandon the standard model and to focus on inhomogeneous cosmologies, and their average evolution. According to this formalism, inhomogeneities within a chosen scale globally impact on the dynamics of this latter through a so-called backreaction effect. This very rich approach also proposes an elegant explanation for the problem of the dark constituents: both stand for an effective manifestation of the inhomogeneities in the distributions of matter and geometry. This thesis focusses on the properties of averaged inhomogeneous models in general relativity. We first propose to describe the global behaviour of inhomogeneities according to a Chaplygin evolution, and according to a Ginzburg-Landau evolution. We also show the global gravitational instability of Friedmann-Lemaître-Robertson-Walker solutions. This class of solutions is already known to be locally gravitationaly unstable under the introduction of perturbations; here we show qualitatively that it does not furnish, in general, a good approximation as a physical background. We finally present a new relativistic perturbative scheme, in which scalar inhomogeneities evolve on a general background rather than on a pre-defined Friedmann-Lemaître-Robertson-Walker background. This new study extends the framework of application for inhomogeneous cosmologies, and may possibly explain the large-scale structure formation without the need for dark energy

Dans le modèle standard de la cosmologie, la dynamique globale de l'Univers est modélisée par l'intermédiaire d'un espace-temps de référence (ou de fond) fortement symétrique, admettant des sections spatiales homogènes et isotropes. Le couplage entre les sources fluides, homogènes, et l'expansion globale, y est déterminé par les équations d'Einstein de la Relativité Générale. La formation de structures inhomogènes de matière peut également être décrite dans ce modèle. Selon l'époque et l'échelle considérées, cette description est effectuée soit à l'aide d'un schéma perturbatif relativiste supposant une faible déviation de chaque grandeur par rapport au fond homogène imposé, soit au moyen d'une approche newtonienne au sein du même fond en expansion. L'interprétation des observations dans ce modèle suggère cependant une accélération inattendue de l'expansion, qui requiert une nouvelle composante énergétique mal comprise, l' «Énergie Noire», en plus de la Matière Noire. La cosmologie inhomogène a pour but de lever les restrictions imposées par ces modèles sur la géométrie et sur les sources sans sortir du cadre de la Relativité Générale. Cela peut notamment permettre d'améliorer le modèle de formation des structures pour prendre en compte de fortes déviations par rapport à l'homogénéité dans la distribution de matière et dans la géométrie. Cela permet également d'étudier les conséquences dynamiques, appelées effets de rétroaction («backreaction»), du développement local de telles inhomogénéités sur l'expansion à de plus grandes échelles. De telles rétroactions peuvent alors reproduire, au moins partiellement, les comportements attribués à l'Énergie Noire ou à la Matière Noire. Au cours de mon travail de thèse sous la direction de Thomas Buchert, j'ai étudié plusieurs aspects analytiques de la cosmologie inhomogène en Relativité Générale. Je présente ci-dessous les résultats de travaux au sein de collaborations, auxquels j'ai apporté des contributions majeures dans le cadre de la thèse. Je me suis tout d'abord concentré sur l'écriture d'un schéma d'approximation relativiste lagrangien, pour décrire la dynamique locale des structures jusqu'à un régime non-linéaire, dans des fluides parfaits barotropes irrotationnels. Je me suis ensuite intéressé à la description effective de fluides inhomogènes admettant un tenseur d'énergie-impulsion général ainsi que de la vorticité, au moyen de deux schémas possibles de moyenne spatiale. Ces schémas s'appliquent à un choix quelconque des hypersurfaces spatiales sur lesquelles moyenner, et fournissent pour chacun de ces choix un système d'équations d'évolution effectives, présentant plusieurs termes de rétroaction, pour un domaine d'intégration suivant la propagation des sources. Cela permet une discussion qualitative de la dépendance au choix du feuilletage des équations moyennes et des rétroactions. J'ai également étudié la réécriture de ces schémas de moyennes et équations d'évolution, et d'autres obtenus de façon similaire, sous une forme unifiée et manifestement 4-covariante. Ce dernier résultat permettra une étude plus explicite de la dépendance au feuilletage / In the standard model of cosmology, the global dynamics of the Universe is modelled via a highly symmetric background spacetime with homogeneous and isotropic spatial sections. The coupling of the homogeneous fluid sources to the overall expansion is then determined by the Einstein equations of General Relativity. In addition, the formation of inhomogeneous matter structures is described either via a relativistic perturbation scheme assuming small deviations of all fields to the prescribed homogeneous background, or using Newtonian dynamics within the same expanding background, depending on the scale and epoch. However, the interpretation of observations within this model calls for an unexpectedly accelerated expansion requiring a poorly-understood `Dark Energy' component, in addition to Dark Matter. Inhomogeneous cosmology aims at relaxing the restrictions of these models on the geometry and sources while staying within the framework of General Relativity. It can allow, in particular, for an improved modelling of the formation of structures accounting for strong deviations from homogeneity in the matter distribution and the geometry. It can also study the dynamical consequences, or backreaction effects, of the development of such inhomogeneities on the expansion of larger scales. Such a backreaction may then reproduce, at least partially, the behaviours attributed to Dark Energy or Dark Matter. During my PhD under the direction of Thomas Buchert, I have been working on several analytical aspects of general-relativistic inhomogeneous cosmology. I present below the results of collaborations in which I played a major role in the context of the PhD. I first focussed on the expression of a relativistic Lagrangian approximation scheme for the description of the local dynamics of structures up to a nonlinear regime in irrotational perfect barotropic fluids. I then considered the effective description of inhomogeneous fluids with vorticity and a general energy-momentum tensor in terms of two possible schemes of spatial averaging. These schemes are applicable to any choice of spatial hypersurfaces of averaging, providing for each choice a set of effective evolution equations, featuring several backreaction terms, for an averaging region comoving with the sources. This allows for a qualitative discussion of the dependence of the average equations and backreactions on the foliation choice. I also studied the rewriting of such averaging schemes and evolution equations under a unified and manifestly 4-covariant form. This latter result will allow for a more explicit investigation of foliation dependence