No abstract

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 investigate f (R, T ) gravity models (where R is the curvature scalar and T is the trace of the stress-energy tensor of ordinary matter) that are able to reproduce the four known types of future finite-time singularities. We choose a suitable expression for the Hubble parameter in order to realise the cosmic acceleration and we introduce two parameters, α and H s , which characterise each type of singularity. We address conformal anomaly and we observe that it cannot remove the Sudden Singularity or the Big Brake, but, for some values of α, the Big Rip and the Big Freeze may be avoided. We also find that, even without taking into account conformal anomaly, the Big Rip and the Big Freeze may be removed thanks to the presence of the T contribution of the f (R, T ) theory.Pacs numbers: 04.50. Kd, 95.35.+d, 95.36.+x, 98.80.Qc

We review the difficulties of the generalized Chaplygin gas model to fit observational data, due to the tension between background and perturbative tests. We argue that such issues may be circumvented by means of a self-interacting scalar field representation of the model. However, this proposal seems to be successful only if the self-interacting scalar field has a non-canonical form. The latter can be implemented in Rastall's theory of gravity, which is based on a modification of the usual matter conservation law. We show that, besides its application to the generalized Chaplygin gas model, other cosmological models based on Rastall's theory have many interesting and unexpected new features.PACS numbers: 04.50. Kd, 95.35.+d, 95.36.+x, 98.80.-k * Based on a talk presented by Júlio C. Fabris during the IWARA 2011 conference.

We find exact power-law solutions for scalar-tensor theories and clarify the conditions under which they can account for an accelerated expansion of the Universe. These solutions have the property that the signs of both the Hubble rate and the deceleration parameter in the Jordan frame may be different from the signs of their Einstein-frame counterparts. For special parameter combinations we identify these solutions with asymptotic attractors that have been obtained in the literature through dynamical-system analysis. We establish an effective general-relativistic description for which the geometrical equivalent of dark energy is associated with a time dependent equation of state. The present value of the latter is consistent with the observed cosmological ``constant". We demonstrate that this type of power-law solutions for accelerated expansion cannot be realized in f(R) theories.Comment: 22 pages, 1 figure, substantially rewritten, presentation improved. Accepted for publication in Phys.Rev.