A Brief Review of the Singularities in 4D and 5D Viscous Cosmologies Near the Future Singularity

TL;DR

This paper analyzes the behavior of physical quantities near future singularities in 4D and 5D viscous cosmologies, exploring how viscosity influences the transition from quintessence to phantom regimes and the propagation of singularities.

Contribution

It investigates the effects of bulk viscosity on singularities in both Einstein and modified gravity within 4D and 5D cosmological models, including the Randall-Sundrum II framework.

Findings

Viscosity can induce transition from quintessence to phantom regions.

Singularities on the brane extend into the bulk in 5D models.

The behavior of physical quantities near singularities is affected by the viscosity proportionality to scalar expansion.

Abstract

Analytic properties of physical quantities in the cosmic fluid such as energy density \rho(t) and Hubble parameter H(t) are investigated near the future singularity (Big Rip). Both 4D and 5D cosmologies are considered (the Randall-Sundrum II model in the 5D case), and the fluid is assumed to possess a bulk viscosity \zeta. We consider both Einstein gravity and modified gravity, where in the latter case the Lagrangian contains a term R^\alpha with \alpha a constant. If \zeta is proportional to the power (2\alpha-1) of the scalar expansion, the fluid can pass from the quintessence region into the phantom region as a consequence of the viscosity. A property worth noticing is that the 4D singularity on the brane becomes carried over to the bulk region.