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. I. INTRODUCTIONA host of observations concord with the existence of a dark energy component with negative pressure, accounting for more than two thirds of the current energy budget. The evidence comes, for instance, from measurements of the cosmic microwave background temperature anisotropy [1] and Type Ia supernovae [2]. While the data is so far consistent with the dark fluid being a cosmological constant, it is nevertheless interesting to consider the possibility that near future observations will reveal that w differs from −1.Having w = −1 implies that a parameter of the effective Lagrangian, namely the vacuum energy, is time-dependent.It follows from general covariance and locality that it must also be a function of space; in other words, the vacuum energy is a field, assumed for simplicity to be a fundamental scalar φ. Scalar field models of dark energy generally come under the label of quintessence [3]. Of course, this argument assumes that gravity is described by General Relativity (GR) for all relevant scales, and it is conceivable that the observed acceleration could result from a break down of GR on large scales [4,5,6]. However, we focus on the former possibility.

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 hyper-surface (a so-called brane), which is embedded in a higherdimensional 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 space-time. 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 space-time 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.

Abstract. We study the spherical collapse model in dark energy cosmologies, in which dark energy is modelled as a minimally coupled scalar field. We first follow the standard assumption that dark energy does not cluster on the scales of interest. Investigating four different popular potentials in detail, we show that the predictions of the spherical collapse model depend on the potential used. We also investigate the dependence on the initial conditions. Secondly, we investigate in how far perturbations in the quintessence field affect the predictions of the spherical collapse model. In doing so, we assume that the field collapses along with the dark matter. Although the field is still subdominant at the time of virialisation, the predictions are different from the case of a homogeneous dark energy component. This will in particular be true if the field is non-minimally coupled. We conclude that a better understanding of the evolution of dark energy in the highly non-linear regime is needed in order to make predictions using the spherical collapse model in models with dark energy.

We analyse f (R) modifications of Einstein's gravity as dark energy models in the light of their connection with chameleon theories. Formulated as scalar-tensor theories, the f (R) theories imply the existence of a strong coupling of the scalar field to matter. This would violate all experimental gravitational tests on deviations from Newton's law. Fortunately, the existence of a matter dependent mass and a thin shell effect allows one to alleviate these constraints. The thin shell condition also implies strong restrictions on the cosmological dynamics of the f (R) theories. As a consequence, we find that the equation of state of dark energy is constrained to be extremely close to −1 in the recent past. We also examine the potential effects of f (R) theories in the context of the Eöt-wash experiments. We show that the requirement of a thin shell for the test bodies is not enough to guarantee a null result on deviations from Newton's law. As long as dark energy accounts for a sizeable fraction of the total energy density of the Universe, the constraints which we deduce also forbid any measurable deviation of the dark energy equation of state from -1. All in all, we find that both cosmological and laboratory tests imply that f (R) models are almost coincident with a ΛCDM model at the background level.PACS numbers: 04.50. Kd, 95.36.+x, 12.20.Fv