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

In this paper we explore the different types of singularities that arise in the $Λ$CDM model when dissipative processes are considered, in the framework of the Eckart's theory. In particular, we study the late-time behavior of $Λ$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) $p=(γ-1)ρ$, where $p$ is the equilibrium pressure of the fluid, $ρ$ their energy density, and $γ$ is the barotropic index. We explore two particular cases for the bulk viscosity $ξ$, a constant bulk viscosity $ξ=ξ_{0}$, and a bulk viscosity proportional to the energy density of the fluid $ξ=ξ_{0}ρ$. 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.

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