Bouncing solutions from generalized EoS

Abstract

We present an exact analytical bouncing solution for a closed universe filled with only one exotic fluid with negative pressure, obeying a Generalized Equations of State (GEoS) of the form $P(ρ)=Aρ+Bρ^λ$, where $A$, $B$ and $λ$ are constants. In our solution $A=-1/3$ and $λ=1/2$ and $B<0$ is kept as a free parameter. For particular values of the initial conditions, we obtain that our solution obeys Null Energy Condition (NEC), which allows us to reinterpret the matter source as that of a real scalar field, $ϕ$, with a positive kinetic energy and a potential $V(ϕ)$. We compute numerically the scalar field as a function of time as well as its potential $V(ϕ)$, and find an analytical function for the potential that fits very accurately with the numerical results obtained. The shape of this potential can be well described by a Gaussian-type of function, and hence, there is no spontaneous symmetry minimum of $V(ϕ)$. We further show that the bouncing scenario is structurally stable under small variations of the parameter $A$, such that a family of bouncing solutions can be find numerically, in a small vicinity of the value $A=-1/3$.

12 pages, 12 figures