Singularities and soft-Big Bang in a viscous <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Λ</mml:mi><mml:mi>CDM</mml:mi></mml:math> model
Norman Cruz, Esteban González, José Jovel
Abstract
In this paper we explore the different types of singularities that arise in the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model when dissipative processes are considered, in the framework of the Eckart's theory. In particular, we study the late-time behavior of $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ 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) $p=(\ensuremath{\gamma}\ensuremath{-}1)\ensuremath{\rho}$, where $p$ is the equilibrium pressure of the fluid, $\ensuremath{\rho}$ their energy density, and $\ensuremath{\gamma}$ is the barotropic index. We explore two particular cases for the bulk viscosity $\ensuremath{\xi}$, a constant bulk viscosity $\ensuremath{\xi}={\ensuremath{\xi}}_{0}$, and a bulk viscosity proportional to the energy density of the fluid $\ensuremath{\xi}={\ensuremath{\xi}}_{0}\ensuremath{\rho}$. Due to some previous investigations that have explored how 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 with 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 anti--de Sitter (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.