Bouncing solutions from generalized EoS

Abstract

Abstract We present an exact analytical bouncing solution for a closed universe filled with only one exotic fluid with negative pressure, obeying a generalized equation of state (GEoS) of the form $$p(\rho )=A\rho +B\rho ^{\lambda }$$ p ( ρ ) = A ρ + B ρ λ , where A, B and $$\lambda $$ λ are constants. In our solution $$A=-1/3$$ A = - 1 / 3 , $$\lambda =1/2$$ λ = 1 / 2 , and $$B<0$$ B < 0 is kept as a free parameter. For particular values of the initial conditions, we find that our solution obeys the null energy condition (NEC), which allows us to reinterpret the matter source as that of a real scalar field, $$\phi $$ ϕ , with a positive kinetic energy and a potential $$V(\phi )$$ V ( ϕ ) . We numerically compute the scalar field as a function of time as well as its potential $$V(\phi )$$ V ( ϕ ) , and we find an analytical function for the potential that fits very accurately with the numerical data 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 $$V(\phi )$$ V ( ϕ ) . We show numerically that the bouncing scenario is structurally stable in a small vicinity of the value $$A=-1/3$$ A = - 1 / 3 . We also include the study of the evolution of the linear fluctuations due to linear perturbations in the metric. These perturbations show an oscillatory behavior near the bouncing and approach a constant at large scales.