Cosmological evolution with quadratic gravity and nonideal fluids

TL;DR

This paper explores cosmological models with quadratic gravity and non-ideal fluids, revealing fixed points for different cosmic epochs and analyzing stability, singularities, and the effects of fluid equations of state.

Contribution

It introduces a unified dynamical system framework for quadratic gravity with various non-ideal fluids, identifying key fixed points and stability properties.

Findings

Models include inflationary, radiation, and late-time acceleration fixed points.

Redlich-Kwong fluid admits a second radiation epoch and a Big Rip singularity.

Physical constraints eliminate ghost and tachyonic instabilities.

Abstract

Some cosmological models based on the gravitational theory $f(R) = R+\zeta R^2$, and on fluids obeying to the equations of state of Redlich-Kwong, Berthelot, and Dieterici are proposed for describing smooth transitions between different cosmic epochs. A dynamical system analysis reveals that these models contain fixed points which correspond to an inflationary, a radiation dominated and a late-time accelerating epoch, and a nonsingular bouncing solution, the latter being an asymptotic fixed point of the compactified phase space. The infinity of the compactified phase space is interpreted as a region in which the non-ideal behaviors of the previously mentioned cosmic fluids are suppressed. Physical constraints on the adopted dimensionless variables are derived by demanding the theory to be free from ghost and tachyonic instabilities, and a novel cosmological interpretation of such variables is proposed through a cosmographic analysis. The different effects of the equation of state parameters on the number of equilibrium solutions and on their stability nature are clarified. Some generic properties of these models, which are not sensitive to the particular fluid considered, are identified, while differences are critically examined by showing that the Redlich-Kwong scenario admits a second radiation-dominated epoch and a Big Rip Singularity.