Rastall's theory is a modification of General Relativity, based on the non-conservation of the stress-energy tensor. The latter is encoded in a parameter γ such that γ = 1 restores the usual ∇ ν T µν = 0 law. We test Rastall's theory in cosmology, on a flat Robertson-Walker metric, investigating a two-fluid model and using the type Ia supernovae Constitution dataset. One of the fluids is pressureless and obeys the usual conservation law, whereas the other is described by an equation of state p x = w x ρ x , with w x constant. The Bayesian analysis of the Constitution set does not strictly constrain the parameter γ and prefers values of w x close to −1. We then address the evolution of small perturbations and show that they are dramatically unstable if w x = −1 and γ = 1, i.e. General Relativity is the favored configuration. The only alternative is w x = −1, for which the dynamics becomes independent from γ. *

We use the framework of a recently proposed model of reduced relativistic gas (RRG) to obtain the bounds for Ω's of Dark Matter and Dark Energy (in the present case, a cosmological constant), taking into consideration an arbitrary warmness of Dark Matter. An equivalent equation of state has been used by Sakharov to predict the oscillations in the matter power spectrum. Two kind of tests are accounted for in what follows, namely the ones coming from the dynamics of the conformal factor of the homogeneous and isotropic metric and also the ones based on linear cosmic perturbations. The RRG model demonstrated its high effectiveness, permitting to explore a large volume in the space of mentioned parameters in a rather economic way. Taking together the results of such tests as Supernova type Ia (Union2 sample), H(z), CMB (R factor), BAO and LSS (2dfGRS data), we confirm that ΛCDM is the most favored model. At the same time, for the 2dfGRS data alone we found that an alternative model with a very small quantity of a Dark Matter is also viable. This output is potentially relevant in view of the fact that the LSS is the only test which can not be affected by the possible quantum contributions to the low-energy gravitational action.

We study the matter density fluctuations in the running cosmological constant (RCC) model using linear perturbations in the longitudinal gauge. Using this observable, we calculate the growth rate of structures and the matter power spectrum, and compare these results to SDSS data and the available data for linear growth rate. The distribution of collapsed structures may also constrain models of dark energy. It is shown that the RCC model enhances departures from the ΛCDM model for both cluster number and cumulative cluster number predicted. In general, increasing the characteristic parameter ν leads to significant growth of the cluster number. We found that the theory of perturbations provides a useful tool to distinguish between the new model RCC and the standard cosmological model ΛCDM.

In the Friedmann cosmology, the deceleration of the expansion q plays a fundamental role. We derive the deceleration as a function of redshift q(z) in two scenarios: CDM model and modified Chaplygin gas (MCG) model. The function for the MCG model is then fitted to the cosmological data in order to obtain the cosmological parameters that minimize χ 2 . We use the Fisher matrix to construct the covariance matrix of our parameters and reconstruct the q(z) function. We use Supernovae Ia, WMAP5, and BAO measurements to obtain the observational constraints. We determined the present acceleration as q 0 = −0.65 ± 0.19 for the MCG model using the Union2 dataset of SNeIa, BAO, and CMB and q 0 = −0.67 ± 0.17 for the Constitution dataset, BAO and CMB. The transition redshift from deceleration to acceleration was found to be around 0.80 for both datasets. We have also determined the dark energy parameter for the MCG model: X0 = 0.81 ± 0.03 for the Union2 dataset and X0 = 0.83 ± 0.03 using the Constitution dataset.

The quantum contributions to the gravitational action are relatively easy to calculate in the higher derivative sector of the theory. However, the applications to the postinflationary cosmology and astrophysics require the corrections to the Einstein-Hilbert action and to the cosmological constant, and those we can not derive yet in a consistent and safe way. At the same time, if we assume that these quantum terms are covariant and that they have relevant magnitude, their functional form can be defined up to a single free parameter, which can be defined on the phenomenological basis. It turns out that the quantum correction may lead, in principle, to surprisingly strong and interesting effects in astrophysics and cosmology a .