Scalar-tensor theory with Lagrange multipliers: a way of understanding the cosmological constant problem, and future singularities

TL;DR

This paper explores a scalar-tensor theory with Lagrange multipliers to control the cosmological constant and analyze future singularities, offering new methods for cosmological solution reconstruction and modified gravity models.

Contribution

It introduces a formalism using Lagrange multipliers to constrain scalar fields, enabling the relaxation of the cosmological constant and studying singularities in scalar-tensor theories.

Findings

Reconstruction of cosmological solutions controlling the cosmological constant

Extension to phantom scalar fields with future singularities

Conformal transformation to modified gravity in Jordan frame

Abstract

The use of Lagrange multipliers in the context of quintessence/phantom scalar fields allows to constrain the behavior of the scalar field, which provides a powerful tool, not only for the reconstruction of cosmological solutions but also for the study of some problems in cosmology and gravitational physics. In the present paper, we focus on the reconstruction of cosmological solutions capable of controlling the cosmological constant value by imposing a constraint on the scalar field, providing a relaxation mechanism of the value of the cosmological constant. The formalism is also extended to the study of phantom scalar fields with a future singularity and their conformal transformation to the Jordan frame, where a type of modified gravity, constrained by the Lagrange multiplier, is obtained.