Cosmological dynamics of Scalar--Tensor Gravity

We study the phase--space of FLRW models derived from Scalar--Tensor Gravity where the non--minimal coupling is $F(\phi)=\xi\phi^2$ and the effective potential is $V(\phi)=\lambda \phi^n$. 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 $V(\phi)$. 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.Comment: 25 pages, 4 figures, 12 tables, submitted to CQ

Cosmological dynamics of exponential gravity

We present a detailed investigation of the cosmological dynamics based on $\exp (-R/{\Lambda})$ gravity. We apply the dynamical system approach to both the vacuum and matter cases and obtain exact solutions and their stability in the finite and asymptotic regimes. The results show that cosmic histories exist which admit a double de-Sitter phase which could be useful for describing the early and the late-time accelerating universe.Comment: 17 pages LaTeX, 3 figure

Compactifying the state space for alternative theories of gravity

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--expansion--normalised variables were used. In both examples we comment on the existence of bouncing or recollapsing orbits as well as the existence of static models.Comment: 18 pages, revised to match published versio

Dynamics of f(R)-cosmologies containing Einstein static models

We study the dynamics of homogeneous isotropic FRW cosmologies with positive spatial curvature in $f(R)$-gravity, paying special attention to the existence of Einstein static models and only study forms of $f(R)=R^n$ for which these static models have been shown to exist. We construct a compact state space and identify past and future attractors of the system and recover a previously discovered future attractor corresponding to an expanding accelerating model. We also discuss the existence of universes which have both a past and future bounce, a phenomenon which is absent in General Relativity.Comment: 14 pages, 6 figure

Reconstruction of the Scalar-Tensor Lagrangian from a LCDM Background and Noether Symmetry

We consider scalar-tensor theories and reconstruct their potential U(\Phi) and coupling F(\Phi) by demanding a background LCDM cosmology. In particular we impose a background cosmic history H(z) provided by the usual flat LCDM parameterization through the radiation (w_{eff}=1/3), matter (w_{eff}=0) and deSitter (w_{eff}=-1) eras. The cosmological dynamical system which is constrained to obey the LCDM cosmic history presents five critical points in each era, one of which corresponding to the standard General Relativity (GR). In the cases that differ from GR, the reconstructed coupling and potential are of the form F(\Phi)\sim \Phi^2 and U(\Phi)\sim F(\Phi)^m where m is a constant. This class of scalar tensor theories is also theoretically motivated by a completely independent approach: imposing maximal Noether symmetry on the scalar-tensor Lagrangian. This approach provides independently: i) the form of the coupling and the potential as F(\Phi)\sim \Phi^2 and U(\Phi)\sim F(\Phi)^m, ii) a conserved charge related to the potential and the coupling and iii) allows the derivation of exact solutions by first integrals of motion.Comment: Added comments, discussion, references. 15 revtex pages, 5 fugure

The phase space view of f(R) gravity

We study the geometry of the phase space of spatially flat Friedmann-Lemaitre-Robertson-Walker models in f(R) gravity, for a general form of the function f(R). The equilibrium points (de Sitter spaces) and their stability are discussed, and a comparison is made with the phase space of the equivalent scalar-tensor theory. New effective Lagrangians and Hamiltonians are also presented.Comment: 14 pages, 2 figures, published in Classical and Quantum Gravity; references adde