Cosmological dynamics and dark energy with a nonlinear equation of state: A quadratic model

Abstract

We investigate the general relativistic dynamics of Robertson-Walker models with a non-linear equation of state (EoS), focusing on the quadratic case P = P0 + αρ + βρ 2 . This may be taken to represent the Taylor expansion of any arbitrary barotropic EoS, P (ρ). With the right combination of P0, α and β, it serves as a simple phenomenological model for dark energy, or even unified dark matter. Indeed we show that this simple model for the EoS can produce a large variety of qualitatively different dynamical behaviors that we classify using dynamical systems theory. An almost universal feature is that accelerated expansion phases are mostly natural for these non-linear EoS's. These are often asymptotically de Sitter thanks to the appearance of an effective cosmological constant. Other interesting possibilities that arise from the quadratic EoS are closed models that can oscillate with no singularity, models that bounce between infinite contraction/expansion and models which evolve from a phantom phase, asymptotically approaching a de Sitter phase instead of evolving to a "Big Rip". In a second paper we investigate the effects of the quadratic EoS in inhomogeneous and anisotropic models, focusing in particular on singularities.PACS numbers: 98.80. Jk, 95.35.+d, 95.36.+x

Exact nonlinear inhomogeneities inΛCDMcosmology

“…It can also be used in perturbative studies of the behavior of inhomogeneities and anisotropies in the neighborhood of isotropic singularities for more general space-times such as Bianchi models, see e.g. [69,70].…”

Late universe dynamics with scale-independent linear couplings in the dark sector

“…[21,22,23,24] for a detailed analysis of the cosmological dynamics arising in this case). As we will see, it turns out that there are solutions of the system (9-10) that evolve according to (14).…”

“…To our knowledge, such an exhaustive analysis has not been carried out yet, although several sub-cases have been considered [38,39,40,41,42,43,44]. In our study, we restrict ourselves to the evolution of a homogeneous, isotropic cosmological background, leaving aside the question of what the effects of coupling could be in anisotropic models [23], or when general perturbations are present [45,46]. It is however worth noticing that, thanks to the particular form of coupling we choose, our analysis of the dynamics of the two components is valid in any theory of gravity, because is based only on the conservation equations, and not on specific field equations.…”

“…For example, in [21] we have considered observational constraints on a UDM model with an "affine" EoS, i.e. such that the pressure satisfies the affine relation P = P o + αρ with the energy density [22,23]. This model is a one parameter (α) generalization of ΛCDM, with the latter recovered for α = 0.…”

“…To this end we will use standard dynamical system techniques [29,30], which are now rather common in the analysis of cosmological models, see e.g. [31,32,33,34,35,36] and [22,23,37,38]. To our knowledge, such an exhaustive analysis has not been carried out yet, although several sub-cases have been considered [38,39,40,41,42,43,44].…”