Cosmological dynamics of R ⁿ gravity

Abstract

Abstract.A detailed analysis of dynamics of cosmological models based on R n gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical system theory. In absence of perfect fluid matter, we find exact solutions whose behavior and stability are analyzed in terms of the values of the parameter n. When matter is introduced, the nature of the (non-minimal) coupling between matter and higher order gravity induces restrictions on the allowed values of n. Selecting such intervals of values and following the same procedure used in the vacuum case, we present exact solutions and analyze their stability for a generic value of the parameter n. From this analysis emerges the result that for a large set of initial conditions an accelerated expansion is an attractor for the evolution of the R n cosmology. When matter is present a transient almost-Friedman phase can also be present before the transition to an accelerated expansion.

Large scale structure constraints for a class off(R)theories of gravity

“…Here we give the equations for dust and radiation, while those for a general barotropic equation of state w are presented in [17]:…”

“…Theses difficulties can be reduced somewhat by using the theory of dynamical systems [16], which, with careful choice of dynamical variables, provides a relatively simple method for obtaining exact solutions (via the equilibrium points of the system) and a description of the global dynamics of these models for a given f (R) theory [17].…”

Tidal forces inf(R)theories of gravity

“…We therefore employ a general dynamical systems strategy, following [36,37], to significantly simplify the system of equations. For example, rewriting the Friedmann equation at (20) in the following way:…”

Dynamical instability of collapsing stars in the framework of Rn gravity

“…power-law inflation and ordinary inflation with a minimally coupled scalar field. In the literature, this model is mostly pursued for n = −1 and 3/2 (Capozziello et al 2003;Carloni et al 2005), where it is conformally equivalent to Liouville field theory (Capozziello et al 2003).…”

“…However, only some of them satisfy both the theoretical viability criteria and experimental constraints (De Felice & Tsujikawa 2010;Sotiriou & Faraoni 2010). One of such choices is the model f(R) = R n , where n is not restricted to be an integer (Carloni et al 2005;Capozziello, Cardone & Troisi 2006;Clifton 2006;Leach, Carloni & Dunsby 2006;Bisabr 2010;Leon & Saridakis 2011). This model, like any f(R) model, is subject to experimental constraints; however, from the mathematical point of view, it is absolutely satisfactory to explore this theory as a toy model.…”