Philippe Brax

Quintessence and supergravity

Abstract In the context of quintessence, the concept of tracking solutions allows to address the fine-tuning and coincidence problems. When the field is on tracks today, one has Q ≈ m Pl demonstrating that, generically, any realistic model of quintessence must be based on supergravity. We construct the most simple model for which the scalar potential is positive. The scalar potential deduced from the supergravity model has the form V(Q)= Λ 4+α Q α e κ 2 Q 2 . We show that despite the appearance of positive powers of the field, the coincidence problem is still solved. If α ≥11, the fine-tuning problem can be overcome. Moreover, due to the presence of the exponential term, the value of the equation of state, ω Q , is pushed towards the value −1 in contrast to the usual case for which it is difficult to go beyond ω Q ≈−0.7. For Ω m ≈0.3 , the model presented here predicts ω Q ≈−0.82. Finally, we establish the Ω m −ω Q relation for this model.

Detecting dark energy in orbit: The cosmological chameleon

We show that the chameleon scalar field can drive the current phase of cosmic acceleration for a large class of scalar potentials that are also consistent with local tests of gravity. These provide explicit realizations of a quintessence model where the quintessence scalar field couples directly to baryons and dark matter with gravitational strength. We analyze the cosmological evolution of the chameleon field and show the existence of an attractor solution with the chameleon following the minimum of its effective potential. For a wide range of initial conditions, spanning many orders of magnitude in initial chameleon energy density, the attractor is reached before nucleosynthesis. Surprisingly, the range of allowed initial conditions leading to a successful cosmology is wider than in normal quintessence. We discuss applications to the cyclic model of the universe and show how the chameleon mechanism weakens some of the constraints on cyclic potentials.

Brane world cosmology

Recent developments in the physics of extra dimensions have opened up new avenues to test such theories. We review cosmological aspects of brane world scenarios such as the Randall–Sundrum brane model and two-brane systems with a bulk scalar field. We start with the simplest brane world scenario leading to a consistent cosmology: a brane embedded in an anti-de Sitter space–time. We generalize this setting to the case with a bulk scalar field and then to two-brane systems.We discuss different ways of obtaining a low-energy effective theory for two-brane systems, such as the moduli space approximation and the low-energy expansion. A comparison between the different methods is given. Cosmological perturbations are briefly discussed as well as early universe scenarios such as the cyclic model and the born-again brane world model. Finally we also present some physical consequences of brane world scenarios on the cosmic microwave background and the variation of constants.

Cosmology and brane worlds: a review

Cosmological consequences of the brane world scenario are reviewed in a pedagogical manner. According to the brane world idea, the standard model particles are confined on a hypersurface (a so-called brane), which is embedded in a higher-dimensional spacetime (the so-called bulk). We begin our review with the simplest consistent brane world model: a single brane embedded in a five-dimensional anti-de Sitter spacetime. Then we include a scalar field in the bulk and discuss in detail the difference with the anti-de Sitter case. The geometry of the bulk spacetime is also analysed in some depth. Finally, we investigate the cosmology of a system with two branes and a bulk scalar field. We comment on brane collisions and summarize some open problems of brane world cosmology.

Unified description of screened modified gravity.

We consider modified gravity models driven by a scalar field whose effects are screened in high density regions due to the presence of nonlinearities in its interaction potential and/or its coupling to matter. Our approach covers chameleon, f(R) gravity, dilaton and symmetron models and allows a unified description of all these theories. We find that the dynamics of modified gravity are entirely captured by the time variation of the scalar field mass and its coupling to matter evaluated at the cosmological minimum of its effective potential, where the scalar field has sat since an epoch prior to big bang nucleosynthesis. This new parametrization of modified gravity allows one to reconstruct the potential and coupling to matter and therefore to analyze the full dynamics of the models, from the scale dependent growth of structures at the linear level to nonlinear effects requiring N-body simulations. This procedure is illustrated with explicit examples of reconstruction for chameleon, dilaton, f(R) and symmetron models.

Laboratory tests of the Galileon

The Galileon model is a ghost free scalar effective field theory containing higher derivative terms that are protected by the Galileon symmetry. The presence of a Vainshtein screening mechanism allows the scalar field to couple to matter without mediating unacceptably large fifth forces in the solar system. We describe how laboratory measurements of the Casimir effect and possible deviations from Newtonian gravity can be used to search for Galileon scalar fields. Current experimental measurements are used to bound a previously unconstrained combination of Galileon parameters.

Testing chameleon theories with light propagating through a magnetic field

It was recently argued that the observed PVLAS anomaly can be explained by chameleon field theories in which large deviations from Newtons law can be avoided. Here we present the predictions for the dichroism and the birefringence induced in the vacuum by a magnetic field in these models. We show that chameleon particles behave very differently from standard axionlike particles (ALPs). We find that, unlike ALPs, the chameleon particles are confined within the experimental setup. As a consequence, the birefringence is always bigger than the dichroism in PVLAS-type experiments.

Detecting chameleons through Casimir force measurements

The best laboratory constraints on strongly coupled chameleon fields come not from tests of gravity per se but from precision measurements of the Casimir force. The chameleonic force between two nearby bodies is more akin to a Casimir-like force than a gravitational one: The chameleon force behaves as an inverse power of the distance of separation between the surfaces of two bodies, just as the Casimir force does. Additionally, experimental tests of gravity often employ a thin metallic sheet to shield electrostatic forces; however, this sheet masks any detectable signal due to the presence of a strongly coupled chameleon field. As a result of this shielding, experiments that are designed to specifically test the behavior of gravity are often unable to place any constraint on chameleon fields with a strong coupling to matter. Casimir force measurements do not employ a physical electrostatic shield and as such are able to put tighter constraints on the properties of chameleons fields with a strong matter coupling than tests of gravity. Motivated by this, we perform a full investigation on the possibility of testing chameleon models with both present and future Casimir experiments. We find that present-day measurements are not able to detect the chameleon. However, future experiments have a strong possibility of detecting or rule out a whole class of chameleon models.

Modified gravity tomography.

Abstract We consider the effect of a canonically normalised scalar field degree of freedom on the dynamics of gravity from small to large scales. We show that the effects of modified gravity can be completely captured by the time variations of the scalar field mass and its coupling to matter. This leads to a parameterisation of modified gravity where local constraints are easy to analyse and large scale structure effects apparent.

Systematic simulations of modified gravity: chameleon models

In this work we systematically study the linear and nonlinear structure formation in chameleon theories of modified gravity, using a generic parameterisation which describes a large class of models using only 4 parameters. For this we have modified the N-body simulation code ecosmog to perform a total of 65 simulations for different models and parameter values, including the default ΛCDM. These simulations enable us to explore a significant portion of the parameter space. We have studied the effects of modified gravity on the matter power spectrum and mass function, and found a rich and interesting phenomenology where the difference with the ΛCDM paradigm cannot be reproduced by a linear analysis even on scales as large as k ~ 0.05 hMpc−1, since the latter incorrectly assumes that the modification of gravity depends only on the background matter density. Our results show that the chameleon screening mechanism is significantly more efficient than other mechanisms such as the dilaton and symmetron, especially in high-density regions and at early times, and can serve as a guidance to determine the parts of the chameleon parameter space which are cosmologically interesting and thus merit further studies in the future.