Shear dynamics in Bianchi I cosmologies with R ⁿ -gravity

Abstract

Abstract. We give the equations governing the shear evolution in Bianchi spacetimes for general f (R)-theories of gravity. We consider the case of R ngravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit local rotational symmetry. We find exact solutions and study their behaviour and stability in terms of the values of the parameter n. In particular, we found a set of cosmic histories in which the universe is initially isotropic, then develops shear anisotropies which approaches a constant value.

A dynamical system approach to higher order gravity

“…As in the previous section we will focus on a specific intervals of n referring the reader to [6] for a general analysis. Table 2.…”

“…This means that in these cosmic histories the universe starts in an isotropic state and then develops anisotropies (see figure 1). The presence of an isotropic past attractor is not present in GR and implies that in R n -gravity, like in brane cosmology, there is no need for special initial conditions for inflation to begin [6]. When n > 5/4,Ã is an (isotropic) attractor and all the orbits above the fixed line start on L 1 and converge to it (see Figure 1).…”

“…Of course the issue of determining how many other attractors are present (and so how "probable" this evolution is) is still present and we have to perform a detailed asymptotic analysis in order to understand this point. Using the results of [6] it is possible to show that there are other attractors in the phase space that might influence the global evolution. However, the outcome is that Figure 1.…”

New integrable models and analytical solutions in f(R) cosmology with an ideal gas

“…The modification of the Einstein-Hilbert action by introducing other kind of invariants has lead to an entire menagerie of f -theories [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Some theories are second-order, like general relativity, while others are of at least 4 th order.…”

Dynamical instability of collapsing stars in the framework of Rn gravity

“…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.…”