Cosmology in a model with Lagrange multiplier, and Gauss-Bonnet and non-minimal kinetic couplings

TL;DR

This paper explores a scalar-tensor cosmological model with Gauss-Bonnet and non-minimal kinetic couplings, using a Lagrange multiplier to eliminate ghost modes, and reconstructs scenarios like inflation and dark energy consistent with observations.

Contribution

It introduces a reconstruction method for scalar potential and Lagrange multiplier in models with Gauss-Bonnet and kinetic couplings, ensuring ghost-free and observationally viable cosmologies.

Findings

Viable inflationary models compatible with observational data.

Reconstruction of dark energy scenarios like Little-Rip and de Sitter.

Elimination of ghost modes via Lagrange multiplier constraint.

Abstract

A scalar-tensor model with Gauss-Bonnet and non-minimal kinetic couplings is considered, in which ghost modes are eliminated via a Lagrange multiplier constraint. A reconstruction procedure is deviced for the scalar potential and Lagrange multiplier, valid for any given cosmological scenario. In particular, inflationary and dark energy cosmologies of different types (power-law, Little-Rip, de Sitter, quasi de Sitter) are reconstructed in such models. It is shown that, for various choices of the kinetic coupling terms, it is possible to obtain a viable inflationary phenomenology compatible with the most accurate values of the observational indices.