Cosmological perturbations in Palatini-modified gravity

Abstract

Two approaches to the study of cosmological density perturbations in modified theories of Palatini gravity have recently been discussed. These utilise, respectively, a generalisation of Birkhoff's theorem and a direct linearization of the gravitational field equations. In this paper these approaches are compared and contrasted. The general form of the gravitational lagrangian for which the two frameworks yield identical results in the long-wavelength limit is derived. This class of models includes the case where the lagrangian is a power-law of the Ricci curvature scalar. The evolution of density perturbations in theories of the type f (R) = R − c/R b is investigated numerically. It is found that the results obtained by the two methods are in good agreement on sufficiently large scales when the values of the parameters (b, c) are consistent with current observational constraints. However, this agreement becomes progressively poorer for models that differ significantly from the standard concordance model and as smaller scales are considered.

Viable Palatini-f(R)cosmologies with generalized dark matter

“…(A4), whose effects easily spoil the agreement of these models with observations. This has been extensively discussed elsewhere [31,32,33,34,38] and here we will just discuss the possibilities of alleviating the effects of this scale-dependent term. Let us though note that its presence stems from the new effective matter sources peculiar to the particular class of modified gravity models.…”

Cosmological constraints onf(G) dark energy models

“…Note that the second condition (43) is consistent with the condition (40), which means that if we require an unstable direction for the system to leave the standard matter point P 2 , then P 3 can be a stable phantom-like point, co-existing with the stable de Sitter point P 1 . Which point the universe finally evolves to depends on the initial conditions, as we shall see in Section IV.…”

“…Alternatively, we may consider the Lagrangian density as some general function of the Ricci scalar and the Gauss-Bonnet term √ −gF (R, G) [13,31], and as a natural simplification, F (R, G) = R/2 + f (G) has been investigated [30,[36][37][38][39]. Uddin et al [40] studied the existence and stability of power-law scaling solutions in f (G) models, finding that scaling solutions exist in the model f (G) = ±2 √ αG with α an arbitrary constant. In [41], the authors derived the stability conditions for a de Sitter solution and a standard matter/radiation solution in general f (G) models; the authors also constructed several cosmologically viable f (G) models, but found it difficult to simulate the models to high redshifts.…”

Kantowski-Sachs Cosmological model with quark and strange quark matter in f(R) theory of gravity

“…We know that the power-law relation between scale factor and scalar eld has been used by Johri and Desikan [39], whereas, Kotub Uddin et al [40] have established a result in the context of f (R) gravity which shows…”

“…Recently, this has been used by Sharif and Shamir [19,20]. Now, we solve equation (20) by using a power-law relation between F and a [19,20,39,40] …”