Alain Riazuelo

Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background.

The current ‘standard model’ of cosmology posits an infinite flat universe forever expanding under the pressure of dark energy. First-year data from the Wilkinson Microwave Anisotropy Probe (WMAP) confirm this model to spectacular precision on all but the largest scales. Temperature correlations across the microwave sky match expectations on angular scales narrower than 60° but, contrary to predictions, vanish on scales wider than 60°. Several explanations have been proposed. One natural approach questions the underlying geometry of space—namely, its curvature and topology. In an infinite flat space, waves from the Big Bang would fill the universe on all length scales. The observed lack of temperature correlations on scales beyond 60° means that the broadest waves are missing, perhaps because space itself is not big enough to support them. Here we present a simple geometrical model of a finite space—the Poincaré dodecahedral space—which accounts for WMAPs observations with no fine-tuning required. The predicted density is Ω0 ≈ 1.013 > 1, and the model also predicts temperature correlations in matching circles on the sky.

Exhaustive study of cosmic microwave background anisotropies in quintessential scenarios

Recent high-precision measurements of the CMB anisotropies performed by the BOOMERanG and MAXIMA-1 experiments provide an unmatched set of data allowing us to probe different cosmological models. Among these scenarios, motivated by the recent measurements of the luminosity distance versus redshift relation for type Ia supernovas, is the quintessence hypothesis. It consists of assuming that the acceleration of the Universe is due to a scalar field whose final evolution is insensitive to the initial conditions. Within this framework we investigate the cosmological perturbations for two well-motivated potentials: the Ratra-Peebles and the SUGRA tracking potentials. We show that the solutions of the perturbed equations possess an attractor and that, as a consequence, the insensitivity to the initial conditions is preserved at the perturbed level. Then, we study the predictions of these two models for structure formation and CMB anisotropies and investigate the general features of the multipole moments in the presence of quintessence. We also compare the CMB multipoles calculated with the help of a full Boltzmann code with the BOOMERanG and MAXIMA-1 data. We pay special attention to the location of the second peak and demonstrate that it significantly differs from the location obtained in the cosmological constant case. Finally, we argue that the SUGRA potential is compatible with all the recent data with standard values of the cosmological parameters. In particular, it fits the MAXIMA-1 data better than a cosmological constant or the Ratra-Peebles potential.

Weak lensing in scalar-tensor theories of gravity

This article investigates the signatures of various models of dark energy on weak gravitational lensing, including the complementarity of the linear and nonlinear regimes. It investigates quintessence models and their extension to scalar-tensor gravity. The various effects induced by this simplest extension of general relativity are discussed. It is shown that, given the constraints in the Solar System, models such as a quadratic nonminimal coupling do not leave any signatures that can be detected while other models, such as a runaway dilaton, which include attraction toward general relativity, can let an imprint of about 10%.

Nonvacuum initial states for cosmological perturbations of quantum mechanical origin

In the context of inflation, non-vacuum initial states for cosmological perturbations that possess a built in scale are studied. It is demonstrated that this assumption leads to a falsifiable class of models. The question of whether they lead to conflicts with the available observations is addressed. For this purpose, the power spectrum of the Bardeen potential operator is calculated and compared with the CMBR anisotropies measurements and the redshift surveys of galaxies and clusters of galaxies. Generic predictions of the model are: a high first acoustic peak, the presence of a bump in the matter power spectrum and non-Gaussian statistics. The details are controlled by the number of quanta in the non-vacuum initial state. Comparisons with observations show that there exists a window for the free parameters such that good agreement between the data and the theoretical predictions is possible. However, in the case where the initial state is a state with a fixed number of quanta, it is shown that this number cannot be greater than a few. On the other hand, if the initial state is a quantum superposition, then a larger class of initial states could account for the observations, even though the state cannot be too different from the vacuum. Planned missions such as the MAP and Planck satellites and the Sloan Survey, will demonstrate whether the new class of models proposed here represents a viable alternative to the standard theory.

Cosmic microwave background anisotropies in multiconnected flat spaces

This article investigates the signature of the seventeen multiconnected flat spaces in cosmic microwave background (CMB) maps. For each such space it recalls a fundamental domain and a set of generating matrices, and then goes on to find an orthonormal basis for the set of eigenmodes of the Laplace operator on that space. The basis eigenmodes are expressed as linear combinations of eigenmodes of the simply connected Euclidean space. A preceding work, which provides a general method for implementing multiconnected topologies in standard CMB codes, is then applied to simulate CMB maps and angular power spectra for each space. Unlike in the 3-torus, the results in most multiconnected flat spaces depend on the location of the observer. This effect is discussed in detail. In particular, it is shown that the correlated circles on a CMB map are generically not back to back, so that negative search of back-to-back circles in the Wilkinson Microwave Anisotropy Probe data does not exclude a vast majority of flat or nearly flat topologies.

Correlated mixtures of adiabatic and isocurvature cosmological perturbations

The Cosmic Microwave Background (CMB) anisotropies measurements can provide many clues about the Universe. Although the common belief is that they will allow a very precise measurement of the cosmological parameters (that is, the current state of the Universe), they will alternatively give interesting informations about the state of the initial perturbations (that is, the state of the Universe at the end of inflation). In this paper, we study the observational consequences on the CMB anisotropies of some wide set of inital conditions, with a correlated mixture of adiabatic and isocurvature perturbations.

A new analysis of the Poincaré dodecahedral space model

Context. The full three-year Wilkinson Microwave Anisotropy Probe results (hereafter WMAP3) reinforce the absence of large-angle correlations at scales greater than 60 ◦ . The Poincare dodecahedral space model, which may naturally explain such features, thus remains a plausible cosmological model, despite recent controversy about whether matched circle searches would or would not push the topology beyond the horizon. Aims. We have used new eigenmode calculations of the dodecahedral space to predict the cosmic microwave background (CMB) temperature anisotropies in such a model, with an improved angular resolution. Methods. We have simulated CMB maps and exhibited the expected self intersection of the last scattering surface along six pairs of circles. For a set of plausible cosmological parameters, we have derived the angular power spectrum of the CMB up to large wavenumbers. Results. Comparison of the angular power spectrum with the WMAP3 observations leads to an optimal fit with the Poincare dodecahedral space model, for a value Ωtot = 1.018 of the total energy density parameter.

Simulating cosmic microwave background maps in multiconnected spaces

This paper describes the computation of cosmic microwave background (CMB) anisotropies in a universe with multiconnected spatial sections and focuses on the implementation of the topology in standard CMB computer codes. The key ingredient is the computation of the eigenmodes of the Laplacian with boundary conditions compatible with multiconnected space topology. The correlators of the coefficients of the decomposition of the temperature fluctuation in spherical harmonics are computed and examples are given for spatially flat spaces and one family of spherical spaces, namely, the lens spaces. Under the hypothesis of Gaussian initial conditions, these correlators encode all the topological information of the CMB and suffice to simulate CMB maps.

Quintessence and Gravitational Waves

We investigate some aspects of quintessence models with a nonminimally coupled scalar field and in particular we show that it can behave as a component of matter with

Tracking quintessence by cosmic shear Constraints from VIRMOS-Descart and CFHTLS ⋆ and future prospects

\ensuremath{-}3\ensuremath{\lesssim}P/\ensuremath{\rho}\ensuremath{\lesssim}0.