# Bouncing solutions from generalized EoS

## TL;DR

This paper derives an exact analytical bouncing cosmological solution in a closed universe with a single exotic fluid obeying a generalized equation of state, demonstrating stability and scalar field interpretation.

## Contribution

It introduces a new exact bouncing solution with a specific generalized equation of state and analyzes its stability and scalar field potential.

## Key findings

- Solution obeys Null Energy Condition under certain initial conditions
- Scalar field potential approximates a Gaussian function
- Bouncing solution is stable under small parameter variations

## 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 $P(\rho)=A\rho+B\rho^{\lambda}$, where $A$, $B$ and $\lambda$ are constants. In our solution $A=-1/3$ and $\lambda=1/2$ 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, $\phi$, with a positive kinetic energy and a potential $V(\phi)$. We compute numerically the scalar field as a function of time as well as its potential $V(\phi)$, 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 $V(\phi)$. 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 $A=-1/3$.