Scalar-tensor analysis of an exponential Lagrangian for the Gravitational Field

TL;DR

This paper explores an exponential Lagrangian in modified gravity, analyzing scalar-tensor equivalence, potential minima, and cosmological implications for both positive and negative cosmological constants, including quantum effects.

Contribution

It provides a detailed scalar-tensor analysis of exponential gravity models, including potential minima and quantum regime insights within Loop Quantum Cosmology.

Findings

Potential exhibits a minimum for negative cosmological constant.

DeSitter phase can occur even with negative cosmological constant.

Quantum effects are considered for positive cosmological constant.

Abstract

Within the scheme of modified gravity, an exponential Lagrangian density will be considered, and the corresponding scalar-tensor description will be addressed for both positive and negative values of the cosmological constant. For negative values of the cosmological term, the potential of the scalar field exhibits a minimum, around which scalar-field equations can be linearized. The study of the deSitter regime shows that a comparison with the modified-gravity description is possible in an off-shell region, i.e., in a region where the classical equivalence between the two formulations is not fulfilled. Furthermore, despite the negative cosmological constant, an accelerating deSitter phase is predicted in the region where the series expansion of the exponential term does not hold. For positive values of the cosmological constant, the quantum regime is analyzed within the framework of Loop Quantum Cosmology.