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.
We study the phase-space of FLRW models derived from Scalar-Tensor Gravity where the non-minimal coupling is F (φ) = ξφ 2 and the effective potential is V (φ) = λφ n . Our analysis allows to unfold many feature of the cosmology of this class of theories. For example, the evolution mechanism towards states indistinguishable from GR is recovered and proved to depend critically on the form of the potential V (φ). Also, transient almost-Friedmann phases evolving towards accelerated expansion and unstable inflationary phases evolving towards stable ones are found. Some of our results are shown to hold also for the String-Dilaton action.
Abstract. In this paper we study the dynamics of orthogonal spatially homogeneous Bianchi cosmologies in R n -gravity. We construct a compact state space by dividing the state space into different sectors. We perform a detailed analysis of the cosmological behaviour in terms of the parameter n, determining all the equilibrium points, their stability and corresponding cosmological evolution. In particular, the appropriately compactified state space allows us to investigate static and bouncing solutions. We find no Einstein static solutions, but there do exist cosmologies with bounce behaviours. We also investigate the isotropisation of these models and find that all isotropic points are flat Friedmann like.
In this paper we address important issues surrounding the choice of variables when performing a dynamical systems analysis of alternative theories of gravity. We discuss the advantages and disadvantages of compactifying the state space, and illustrate this using two examples. We first show how to define a compact state space for the class of LRS Bianchi type I models in R n -gravity and compare to a non-compact expansion-normalised approach. In the second example we consider the flat Friedmann matter subspace of the previous example, and compare the compact analysis to studies where non-compact non-expansionnormalised variables were used. In both examples we comment on the existence of bouncing or recollapsing orbits as well as the existence of static models.
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