Fundamental constants and tests of general relativity - Theoretical and cosmological considerations

The tests of the constancy of the fundamental constants are tests of the local position invariance and thus of the equivalence principle. We summarize the various constraints that have been obtained and then describe the connection between varying constants and extensions of general relativity. To finish, we discuss the link with cosmology, and more particularly with the acceleration of the Universe. We take the opportunity to summarize various possibilities to test general relativity (but also the Copernican principle) on cosmological scales.Comment: Proceedings of the workshop ``The nature of gravity, confronting theory and experiment in space'', ISSI, Bern, october 200

Weak lensing B-modes on all scales as a probe of local isotropy

This article derives a multipolar hierarchy for the propagation of the weak-lensing shear and convergence in a general spacetime. The origin of B-modes, in particular on large angular scales, is related to the local isotropy of space. Known results assuming a Friedmann-Lema\^itre background are naturally recovered. The example of a Bianchi I spacetime illustrates our formalism and its implications for future observations are stressed.Comment: 10 pages, 2 figures. Replaced to match published versio

Manifestations of a spatial variation of fundamental constants on atomic clocks, Oklo, meteorites, and cosmological phenomena

The remarkable detection of a spatial variation in the fine-structure constant, alpha, from quasar absorption systems must be independently confirmed by complementary searches. In this letter, we discuss how terrestrial measurements of time-variation of the fundamental constants in the laboratory, meteorite data, and analysis of the Oklo nuclear reactor can be used to corroborate the spatial variation seen by astronomers. Furthermore, we show that spatial variation of the fundamental constants may be observable as spatial anisotropy in the cosmic microwave background, the accelerated expansion (dark energy), and large-scale structure of the Universe.Comment: 4 page

Topological Lensing in Spherical Spaces

This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It discusses which spherical topologies are likely to be detectable by crystallographic methods using three-dimensional catalogs of cosmic objects. The expected form of the pair separation histogram is predicted (including the location and height of the spikes) and is compared to computer simulations, showing that this method is stable with respect to observational uncertainties and is well suited for detecting spherical topologies.Comment: 32 pages, 26 figure

Kolmogorov stochasticity parameter measuring the randomness in Cosmic Microwave Background

The Kolmogorov stochasticity parameter (KSP) is applied to quantify the degree of randomness (stochasticity) in the temperature maps of the Cosmic Microwave Background radiation maps. It is shown that, the KSP for the WMAP5 maps is about twice higher than that of the simulated maps for the concordance \LambdaCDM cosmological model, implying the existence of a randomizing effect not taken into account in the model. As was revealed recently, underdense regions in the large scale matter distributions, i.e the voids, possess hyperbolic and hence randomizing properties. The degree of randomness for the Cold Spot appears to be about twice higher than the average over the mean temperature level spots in the sky, which supports the void nature of the Cold Spot. Kolmogorov's parameter then acts as a quantitative tracer of the voids via CMB.Comment: A&A Lett (in press), 2 pages, 1 Tabl

The No-defect Conjecture: Cosmological Implications

When the topology of the universe is non trivial, it has been shown that there are constraints on the network of domain walls, cosmic strings and monopoles. I generalize these results to textures and study the cosmological implications of such constraints. I conclude that a large class of multi-connected universes with topological defects accounting for structure formation are ruled out by observation of the cosmic microwave background.Comment: 4 pages, 1 figure, accepted for publication as a brief report in Phys. Rev.

The acceleration of the universe and the physics behind it

Using a general classification of dark enegy models in four classes, we discuss the complementarity of cosmological observations to tackle down the physics beyond the acceleration of our universe. We discuss the tests distinguishing the four classes and then focus on the dynamics of the perturbations in the Newtonian regime. We also exhibit explicitely models that have identical predictions for a subset of observations.Comment: 18 pages, 18 figure

Cosmic microwave background anisotropies in multi-connected flat spaces

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.Comment: 33 pages, 19 figures, 1 table. Submitted to PR

On the Trace-Free Einstein Equations as a Viable Alternative to General Relativity

The quantum field theoretic prediction for the vacuum energy density leads to a value for the effective cosmological constant that is incorrect by between 60 to 120 orders of magnitude. We review an old proposal of replacing Einstein's Field Equations by their trace-free part (the Trace-Free Einstein Equations), together with an independent assumption of energy--momentum conservation by matter fields. While this does not solve the fundamental issue of why the cosmological constant has the value that is observed cosmologically, it is indeed a viable theory that resolves the problem of the discrepancy between the vacuum energy density and the observed value of the cosmological constant. However, one has to check that, as well as preserving the standard cosmological equations, this does not destroy other predictions, such as the junction conditions that underlie the use of standard stellar models. We confirm that no problems arise here: hence, the Trace-Free Einstein Equations are indeed viable for cosmological and astrophysical applications.Comment: Substantial changes from v1 including added author, change of title and emphasis of the paper although all original results of v1. remai

Theory Challenges of the Accelerating Universe

The accelerating expansion of the universe presents an exciting, fundamental challenge to the standard models of particle physics and cosmology. I highlight some of the outstanding challenges in both developing theoretical models and interpreting without bias the observational results from precision cosmology experiments in the next decade that will return data to help reveal the nature of the new physics. Examples given focus on distinguishing a new component of energy from a new law of gravity, and the effect of early dark energy on baryon acoustic oscillations.Comment: 10 pages, 4 figures; minor changes to match J. Phys. A versio