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+Bρλ, 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.Comment: 12 pages, 12 figure