arXiv subjects
Publications and source records attributed to Jean-Philippe Uzan.
Recent key observational results on the variation of fine structure constant, the proton to electron mass ratio and the gravitational constant are reviewed. The necessity to substantiate the dark sector of cosmology and to test gravity on astrophysical scales is also emphasized.
Cosmologists are taking a renewed interest in multiconnected spherical 3-manifolds (spherical spaceforms) as possible models for the physical universe. To understand the formation of large scale structures in such a universe, cosmologists express physical quantities, such as density fluctuations in the primordial plasma, as linear combinations of the eigenmodes of the Laplacian, which can then be integrated forward in time. This need for explicit eigenmodes contrasts sharply with previous mathematical investigations, which have focused on questions of isospectrality rather than eigenmodes. The present article provides explicit orthonormal bases for the eigenmodes of lens and prism spaces. As a corollary it extends known results on spectra from homogeneous lens spaces L(p,1) [Ikeda 1995] to arbitrary lens spaces L(p,q).
We investigate a possible asymmetry in the statistical properties of the cosmic microwave background temperature field and to do so we construct an estimator aiming at detecting a dipolar modulation. Such a modulation is found to induce correlations between multipoles with $Δ\ell=1$. Applying this estimator, to the V and W bands of the WMAP data, we found a significant detection in the V band. We argue however that foregrounds and in particular point sources are the origin of this signal.
X-ray and Sunyaev-Zel'dovich data of clusters of galaxies enable to construct a test of the distance duality relation between the angular and luminosity distances. We argue that such a test on large cluster samples may be of importance while trying to distinguish between various models of dark energy. The analysis of a data set of 18 clusters shows no significant violation of this relation. The origin and amplitude of systematic effects and the possibility to increase the precision of this method are discussed.
Inflation universally produces classical almost scale free Gaussian inhomogeneities of any light scalars. Assuming the coupling constants at the time of inflation depend on some light moduli fields, we encounter the generation of modulated cosmological fluctuations from (p)reheating. This is an alternative mechanism to generate observable (almost) scale free adiabatic metric perturbations. We extend this idea to the class of hybrid inflation, where the bifurcation value of the inflaton is modulated by the spatial inhomogeneities of the couplings. As a result, the symmetry breaking after inflation occurs not simultaneously in space but with the time laps in different Hubble patches inherited from the long-wavelength moduli inhomogeneities. To calculate modulated fluctuations we introduce techniques of general relativistic matching conditions for metric perturbations at the time hypersurface where the equation of state after inflation undergoes a jump, without evoking the detailed microscopic physics, as far as it justifies the jump. We apply this theory to the modulated fluctuations from the hybrid and chaotic inflations. We discuss what distinguish the modulated from the inflation-driven fluctuations, in particular, their spectral index, modification of the consistency relation and the issue of weak non-Gaussianity.
We present the expressions of the three- and four-point correlation functions of a self interacting light scalar field in a de Sitter spacetime at tree order respectively for a cubic and a quartic potential. Exact expressions are derived and their limiting behaviour on super-horizon scales are presented. Their essential features are shown to be similar to those obtained in a classical approach.
Models of multi-field inflation exhibiting primordial non-Gaussianity have recently been introduced. This is the case in particular if the fluctuations of a light field scalar field, transverse to the inflaton direction, with quartic coupling can be transferred to the metric fluctuations. So far in those calculations only the ensemble statistical properties have been considered. We explore here how finite volume effects could affect those properties. We show that the expected non-Gaussian properties survive at a similar level when the finite volume effects are taken into account and also find that they can skew the metric distribution even though the ensemble distribution is symmetric.
This article investigates the signature of the seventeen multi-connected 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 multi-connected 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 multi-connected 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 WMAP data does not exclude a vast majority of flat or nearly flat topologies.
This article describes the Cosmic Microwave Background anisotropies expected in a closed universe with the topology of a lens space L(p,q) and with density parameter Omega_0 close to 1. It provides the first simulated maps for such spaces along with their corresponding power spectra. In spite of our initial expectations that increasing p (and thus decreasing the size of the fundamental domain) should suppress the quadrupole, we found just the opposite: increasing p elevates the relative power of the low multipoles, for reasons that have since become clear. For Omega_0 = 1.02, an informal ``by eye'' examination of the simulated power spectra suggests that $p$ must be less than 15 for consistency with WMAP's data, while geometric considerations imply that matching circles will exist (potentially revealing the multi-connected topology) only if p > 7. These bounds become less stringent for values of Omega_0 closer to 1.
Theories proposing a varying speed of light have recently been widely promoted under the claim that they offer an alternative way of solving the standard cosmological problems. Recent observational hints that the fine structure constant may have varied during over cosmological scales also has given impetus to these models. In theoretical physics the speed of light, $c$, is hidden in almost all equations but with different facets that we try to distinguish. Together with a reminder on scalar-tensor theories of gravity, this sheds some light on these proposed varying speed of light theories.
Inter alia, the high precision WMAP data on Cosmic Microwave Background Radiation marginally indicate that the universe has positively curved (and hence spherical) spatial sections. In this paper, we take this data seriously and consider some of the consequences for the background dynamics. In particular, we show that this implies a limit to the number of e-foldings that could have taken place in the inflationary epoch; however this limit is consistent with some inflationary models that solve all the usual cosmological problems and are consistent with standard structure formation theory.
It has recently been proposed by Mersini et al. 01, Bastero-Gil and Mersini 02 that the dark energy could be attributed to the cosmological properties of a scalar field with a non-standard dispersion relation that decreases exponentially at wave-numbers larger than Planck scale (k_phys > M_Planck). In this scenario, the energy density stored in the modes of trans-Planckian wave-numbers but sub-Hubble frequencies produced by amplification of the vacuum quantum fluctuations would account naturally for the dark energy. The present article examines this model in detail and shows step by step that it does not work. In particular, we show that this model cannot make definite predictions since there is no well-defined vacuum state in the region of wave-numbers considered, hence the initial data cannot be specified unambiguously. We also show that for most choices of initial data this scenario implies the production of a large amount of energy density (of order M_Planck^4) for modes with momenta of order M_Planck, far in excess of the background energy density. We evaluate the amount of fine-tuning in the initial data necessary to avoid this back-reaction problem and find it is of order H/M_Planck. We also argue that the equation of state of the trans-Planckian modes is not vacuum-like. Therefore this model does not provide a suitable explanation for the dark energy.
This article describes the computation of cosmic microwave background anisotropies in a universe with multi-connected 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 multi-connected 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.
When the density parameter is close to unity, the universe has a large curvature radius independently of its being hyperbolic, flat, or spherical. Whatever the curvature, the universe may have either a simply connected or a multiply connected topology. In the flat case, the topology scale is arbitrary, and there is no a priori reason for this scale to be of the same order as the size of the observable universe. In the hyperbolic case any nontrivial topology would almost surely be on a length scale too large to detect. In the spherical case, by contrast, the topology could easily occur on a detectable scale. The present paper shows how, in the spherical case, the assumption of a nearly flat universe simplifies the algorithms for detecting a multiply connected topology, but also reduces the amount of topology that can be seen. This is of primary importance for the upcoming cosmic microwave background data analysis. This article shows that for spherical spaces one may restrict the search to diametrically opposite pairs of circles in the circles-in-the-sky method and still detect the cyclic factor in the standard factorization of the holonomy group. This vastly decreases the algorithm's run time. If the search is widened to include pairs of candidate circles whose centers are almost opposite and whose relative twist varies slightly, then the cyclic factor along with a cyclic subgroup of the general factor may also be detected. Unfortunately the full holonomy group is, in general, unobservable in a nearly flat spherical universe, and so a full 6-parameter search is unnecessary. Crystallographic methods could also potentially detect the cyclic factor and a cyclic subgroup of the general factor, but nothing else.
We construct explicit models of multi-field inflation in which the primordial metric fluctuations do not necessarily obey Gaussian statistics. These models are realizations of mechanisms in which non-Gaussianity is first generated by a light scalar field and then transferred into curvature fluctuations. The probability distribution functions of the metric perturbation at the end of inflation are computed. This provides a guideline for designing strategies to search for non-Gaussian signals in future CMB and large scale structure surveys.
This article investigates the generation of non-Gaussianity during inflation. In the context of multi-field inflation, we detail a mechanism that can create significant primordial non-Gaussianities in the adiabatic mode while preserving the scale invariance of the power spectrum. This mechanism is based on the generation of non-Gaussian isocurvature fluctuations which are then transfered to the adiabatic modes through a bend in the classical inflaton trajectory. Natural realizations involve quartic self-interaction terms for which a full computation can be performed. The expected statistical properties of the resulting metric fluctuations are shown to be the superposition of a Gaussian and a non-Gaussian contribution of the same variance. The relative weight of these two contributions is related to the total bending in field space. We explicit the non-Gaussian probability distribution function which appears to be described by a single new parameter. Only two new parameters therefore suffice in describing the non-Gaussianity.
The framework for considering the astronomical and cosmological observations in the context of scalar-tensor quintessence in which the quintessence field also accounts for a time dependence of the gravitational constant is developed. The constraints arising from nucleosynthesis, the variation of the constant, and the post-Newtonian measurements are taken into account. A simple model of supernovae is presented in order to extract the dependence of their light curves with the gravitational constant; this implies a correction when fitting the luminosity distance. The properties of perturbations as well as CMB anisotropies are also investigated.
This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on the variation of the fine structure constant, the gravitational, weak and strong interactions couplings and the electron to proton mass ratio are reviewed. This review aims (1) to provide the basics of each measurement, (2) to show as clearly as possible why it constrains a given constant and (3) to point out the underlying hypotheses. Such an investigation is of importance to compare the different results, particularly in view of understanding the recent claims of the detections of a variation of the fine structure constant and of the electron to proton mass ratio in quasar absorption spectra. The theoretical models leading to the prediction of such variation are also reviewed, including Kaluza-Klein theories, string theories and other alternative theories and cosmological implications of these results are discussed. The links with the tests of general relativity are emphasized.