Exact solutions of a full causal bulk viscous FRW cosmological model with variable G and Λ through factorization

Abstract

We study the classical flat full causal bulk viscous FRW cosmological model with variable gravitational and cosmological constants through the factorization method. The method allows us to find some new exact parametric solutions. The assumptions made bring us to study two approaches. We find, in the studied cases, that the Universe ends in an accelerating era except in the case of a particular solution where the Universe could be noninflationary for all times. In both approaches the cosmological constant is a decreasing function of time, while the gravitational constant behaves as a growing or decreasing time function depending on the sign of Λ. By taking into account recent observations that indicate that Λ must be positive, we conclude that G increases with time except in the first solution where both "constants" tend asymptotically in the large time limit to a constant value. We also present a new factorization scheme which allows us to generate new solutions to a kind of variable coefficient nonlinear second order ODE.

Constraining a causal dissipative cosmological model

“…The basic concept follows the same pattern already used in linear equations, and it works efficiently for ODEs with polynomial nonlinearities. The method is well adapted to the Hubble rate ODE which raises for instance in viscous cosmological models [35,36].…”