Singularities and Soft-Big Bang in a viscous $\Lambda$CDM model

TL;DR

This paper investigates the impact of bulk viscosity in a $\Lambda$CDM cosmology, revealing new singularity types, including Soft-Big Bang, and analyzing their conditions in both positive and negative cosmological constant scenarios.

Contribution

It introduces a viscous $\Lambda$CDM model with specific viscosity forms, extending analysis to negative cosmological constants and identifying novel singularity behaviors.

Findings

Future singularities like Big-Rip can occur without phantom dark energy.

Negative cosmological constant allows Big-Crunch, de Sitter, and Big-Rip singularities.

A Soft-Big Bang solution without initial singularity is identified.

Abstract

In this paper we explore the different types of singularities that arise in the $\Lambda$CDM model when dissipative processes are considered, in the framework of the Eckart's theory. In particular, we study the late-time behavior of $\Lambda$CDM model with viscous cold dark matter (CDM) and an early-time viscous radiation domination era with cosmological constant (CC). The fluids are described by the barotropic equation of state (EoS) $p=(\gamma-1)\rho$, where $p$ is the equilibrium pressure of the fluid, $\rho$ their energy density, and $\gamma$ is the barotropic index. We explore two particular cases for the bulk viscosity $\xi$, a constant bulk viscosity $\xi=\xi_{0}$, and a bulk viscosity proportional to the energy density of the fluid $\xi=\xi_{0}\rho$. Due to some previous investigations that have explored to describe the behavior of the universe with a negative CC, we extend our analysis to this case. We found that future singularities like Big-Rip are allowed but without having a phantom EoS associated to the DE fluid. Big-Crunch singularities also appears when a negative CC is present, but also de Sitter and even Big-Rip types are allowed due to the negative pressure of the viscosity, which opens the possibility of an accelerated expansion in AdS cosmologies. We also discuss a very particular solution without Big Bang singularity that arises in the early-time radiation dominant era of our model known as Soft-Big Bang.