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

We investigate the general relativistic dynamics of Robertson-Walker models with a nonlinear equation of state (EoS), focusing on the quadratic case P=Po+αρ+βρ2. This may be taken to represent theTaylor expansion of any arbitrary barotropic EoS, P(ρ). With the right combination of Po, 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 nonlinear 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