Coupled quintessence and curvature-assisted acceleration

Spatially homogeneous models with a scalar field non-minimally coupled to the space-time curvature or to the ordinary matter content are analysed with respect to late-time asymptotic behaviour, in particular to accelerated expansion and isotropization. It is found that a direct coupling to the curvature leads to asymptotic de Sitter expansion in arbitrary exponential potentials, thus yielding a positive cosmological constant although none is apparent in the potential. This holds true regardless of the steepness of the potential or the smallness of the coupling constant. For matter-coupled scalar fields, the asymptotics are obtained for a large class of positive potentials, generalizing the well-known cosmic no-hair theorems for minimal coupling. In this case it is observed that the direct coupling to matter does not impact the late-time dynamics essentially.Comment: 17 pages, no figures. v2: typos correcte

Anisotropic Power-law Inflation

We study an inflationary scenario in supergravity model with a gauge kinetic function. We find exact anisotropic power-law inflationary solutions when both the potential function for an inflaton and the gauge kinetic function are exponential type. The dynamical system analysis tells us that the anisotropic power-law inflation is an attractor for a large parameter region.Comment: 14 pages, 1 figure. References added, minor corrections include

Cosmic no-hair: non-linear asymptotic stability of de Sitter universe

We study the asymptotic stability of de Sitter spacetime with respect to non-linear perturbations, by considering second order perturbations of a flat Robertson-Walker universe with dust and a positive cosmological constant. Using the synchronous comoving gauge we find that, as in the case of linear perturbations, the non-linear perturbations also tend to constants, asymptotically in time. Analysing curvature and other spacetime invariants we show, however, that these quantities asymptotically tend to their de Sitter values, thus demonstrating that the geometry is indeed locally asymptotically de Sitter, despite the fact that matter inhomogeneities tend to constants in time. Our results support the inflationary picture of frozen amplitude matter perturbations that are stretched outside the horizon, and demonstrate the validity of the cosmic no-hair conjecture in the nonlinear inhomogeneous settings considered here.Comment: 8 pages, REVTEX, submitted to Physical Review Lette

Attractor Solution of Phantom Field

In light of recent study on the dark energy models that manifest an equation of state $w<-1$, we investigate the cosmological evolution of phantom field in a specific potential, exponential potential in this paper. The phase plane analysis show that the there is a late time attractor solution in this model, which address the similar issues as that of fine tuning problems in conventional quintessence models. The equation of state $w$ is determined by the attractor solution which is dependent on the $\lambda$ parameter in the potential. We also show that this model is stable for our present observable universe.Comment: 9 pages, 3 ps figures; typos corrected, references updated, this is the final version to match the published versio

Scaling Solutions in Robertson-Walker Spacetimes

We investigate the stability of cosmological scaling solutions describing a barotropic fluid with $p=(\gamma-1)\rho$ and a non-interacting scalar field $\phi$ with an exponential potential V(\phi)=V_0\e^{-\kappa\phi}. We study homogeneous and isotropic spacetimes with non-zero spatial curvature and find three possible asymptotic future attractors in an ever-expanding universe. One is the zero-curvature power-law inflation solution where $\Omega_\phi=1$ ($\gamma2/3,\kappa^2<2$). Another is the zero-curvature scaling solution, first identified by Wetterich, where the energy density of the scalar field is proportional to that of matter with $\Omega_\phi=3\gamma/\kappa^2$ ($\gamma3\gamma$). We find that this matter scaling solution is unstable to curvature perturbations for $\gamma>2/3$. The third possible future asymptotic attractor is a solution with negative spatial curvature where the scalar field energy density remains proportional to the curvature with $\Omega_\phi=2/\kappa^2$ ($\gamma>2/3,\kappa^2>2$). We find that solutions with $\Omega_\phi=0$ are never late-time attractors.Comment: 8 pages, no figures, latex with revte

Late-time oscillatory behaviour for self-gravitating scalar fields

This paper investigates the late-time behaviour of certain cosmological models where oscillations play an essential role. Rigorous results are proved on the asymptotics of homogeneous and isotropic spacetimes with a linear massive scalar field as source. Various generalizations are obtained for nonlinear massive scalar fields, $k$-essence models and $f(R)$ gravity. The effect of adding ordinary matter is discussed as is the case of nonlinear scalar fields whose potential has a degenerate zero.Comment: 17 pages, additional reference

Bianchi type IX asymptotical behaviours with a massive scalar field: chaos strikes back

We use numerical integrations to study the asymptotical behaviour of a homogeneous but anisotropic Bianchi type IX model in General Relativity with a massive scalar field. As it is well known, for a Brans-Dicke theory, the asymptotical behaviour of the metric functions is ruled only by the Brans-Dicke coupling constant with respect to the value -3/2. In this paper we examine if such a condition still exists with a massive scalar field. We also show that, contrary to what occurs for a massless scalar field, the singularity oscillatory approach may exist in presence of a massive scalar field having a positive energy density.Comment: 31 pages, 7 figures (low resolution

Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound

In many cases a nonlinear scalar field with potential $V$ can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for homogeneous spacetimes. It is shown that, under the assumption that $V$ has a strictly positive minimum, Wald's theorem on spacetimes with positive cosmological constant can be generalized to a wide class of potentials. In some cases detailed information on late-time asymptotics is obtained. Results on the behaviour in the past time direction are also presented.Comment: 16 page

Energy Density of Non-Minimally Coupled Scalar Field Cosmologies

Scalar fields coupled to gravity via $\xi R {\Phi}^2$ in arbitrary Friedmann-Robertson-Walker backgrounds can be represented by an effective flat space field theory. We derive an expression for the scalar energy density where the effective scalar mass becomes an explicit function of $\xi$ and the scale factor. The scalar quartic self-coupling gets shifted and can vanish for a particular choice of $\xi$. Gravitationally induced symmetry breaking and de-stabilization are possible in this theory.Comment: 18 pages in standard Late

Tunneling and propagation of vacuum bubbles on dynamical backgrounds

In the context of bubble universes produced by a first-order phase transition with large nucleation rates compared to the inverse dynamical time scale of the parent bubble, we extend the usual analysis to non-vacuum backgrounds. In particular, we provide semi-analytic and numerical results for the modified nucleation rate in FLRW backgrounds, as well as a parameter study of bubble walls propagating into inhomogeneous (LTB) or FLRW spacetimes, both in the thin-wall approximation. We show that in our model, matter in the background often prevents bubbles from successful expansion and forces them to collapse. For cases where they do expand, we give arguments why the effects on the interior spacetime are small for a wide range of reasonable parameters and discuss the limitations of the employed approximations.Comment: 29 pages, 8 figures, typos corrected, matches published versio