Cosmo-dynamics and dark energy with a quadratic EoS: anisotropic models, large-scale perturbations and cosmological singularities

摘要

In general relativity, for fluids with a linear equation of state (EoS) orscalar fields, the high isotropy of the universe requires special initialconditions, and singularities are anisotropic in general. In the brane worldscenario anisotropy at the singularity is suppressed by an effective quadraticequation of state. There is no reason why the effective EoS of matter should belinear at the highest energies, and a non-linear EoS may describe dark energyor unified dark matter (Paper I, astro-ph/0512224). In view of this, here westudy the effects of a quadratic EoS in homogenous and inhomogeneouscosmological models in general relativity, in order to understand if in thiscontext the quadratic EoS can isotropize the universe at early times. Withrespect to Paper I, here we use the simplified EoS P=alpha rho + rho^2/rho_c,which still allows for an effective cosmological constant and phantom behavior,and is general enough to analyze the dynamics at high energies. We first studyanisotropic Bianchi I and V models, focusing on singularities. Using dynamicalsystems methods, we find the fixed points of the system and study theirstability. We find that models with standard non-phantom behavior are ingeneral asymptotic in the past to an isotropic fixed point IS, i.e. in thesemodels even an arbitrarily large anisotropy is suppressed in the past: thesingularity is matter dominated. Using covariant and gauge invariant variables,we then study linear perturbations about the homogenous and isotropic spatiallyflat models with a quadratic EoS. We find that, in the large scale limit, allperturbations decay asymptotically in the past, indicating that the isotropicfixed point IS is the general asymptotic past attractor for non phantominhomogeneous models with a quadratic EoS. (Abridged)