Big Rip and Little Rip solutions in scalar model with kinetic and Gauss Bonnet couplings

TL;DR

This paper explores late-time cosmological solutions in a scalar field model with kinetic and Gauss-Bonnet couplings, analyzing conditions for Big Rip and Little Rip scenarios and reconstructing models matching observed cosmic behavior.

Contribution

It introduces simplified solutions with specific Gauss-Bonnet couplings, enabling reconstruction of cosmological models with or without Big Rip singularities.

Findings

Model simplifies with specific Gauss-Bonnet couplings.

Solutions can match observed equation of state behavior.

Both Big Rip and Little Rip scenarios are possible.

Abstract

Late time cosmological solutions for scalar field model with kinetic and Gauss Bonnet couplings are considered. The quintom scenario is realized with and without Big Rip singularity. We find that under specific choice of the Gauss Bonnet coupling, the model considerable simplifies, giving rise to solutions where the kinetic term is proportional to the square of the Hubble parameter. This allows to reconstruct the model for a suitable cosmological evolution. We considered a solution that matches the observed behavior of the equation of state, while Big Rip singularity may be present or absent, depending on the parameters of the solution. Evolutionary scenarios known as Little Rip, have also been considered.