Gauss-Bonnet dark energy by Lagrange multipliers

TL;DR

This paper explores a string-inspired gravity model with Gauss-Bonnet interactions and Lagrange multipliers to reconstruct cosmological dark energy solutions, including quintessence and phantom types, highlighting the role of Lagrange multipliers in cosmic evolution.

Contribution

It introduces a novel use of Lagrange multipliers in Gauss-Bonnet gravity to achieve cosmological reconstruction and analyze dark energy dynamics.

Findings

Derived exact solutions for various dark energy models.

Showed Lagrange multiplier acts as dust fluid during cosmic transitions.

Compared dynamical approaches with and without Lagrange multipliers.

Abstract

A string-inspired effective theory of gravity, containing Gauss-Bonnet invariant interacting with a scalar field, is considered in view of obtaining cosmological dark energy solutions. A Lagrange multiplier is inserted into the action in order to achieve the cosmological reconstruction by selecting suitable forms of couplings and potentials. Several cosmological exact solutions (including dark energy of quintessence, phantom or Little Rip type) are derived in presence and in absence of the Lagrange multiplier showing the difference in the two dynamical approaches. In the models that we consider, the Lagrange multiplier behaves as a sort of dust fluid that realizes the transitions between matter dominated and dark energy epochs. The relation between Lagrange multipliers and Noether symmetries is discussed.