Dark energy from modified gravity with Lagrange multipliers

TL;DR

This paper explores how Lagrange multiplier constraints in modified gravity theories affect dark energy models, showing that such constraints alter the equivalence with scalar theories and modify cosmological dynamics.

Contribution

It introduces the role of Lagrange multipliers in scalar-tensor and $F(R)$ gravity, revealing how they influence dark energy cosmology and the equivalence between different gravity theories.

Findings

Lagrange multipliers break the mathematical equivalence between scalar theory and $F(R)$ gravity.

The cosmological dynamics in $F(R)$ gravity are modified by an additional function $F_2(R)$ due to the constraint.

Dark energy models can be reconstructed with different epochs, including $ ext{Λ}$CDM and phantom transitions.

Abstract

We study scalar-tensor theory, k-essence and modified gravity with Lagrange multiplier constraint which role is to reduce the number of degrees of freedom. Dark Energy cosmology of different types ($\Lambda$CDM, unified inflation with DE, smooth non-phantom/phantom transition epoch) is reconstructed in such models. It is shown that mathematical equivalence between scalar theory and $F(R)$ gravity is broken due to presence of constraint. The cosmological dynamics of $F(R)$ gravity is modified by the second $F_2(R)$ function dictated by the constraint. Dark Energy cosmology is defined by this function while standard $F_1(R)$ function is relevant for local tests (modification of newton regime). A general discussion on the role of Lagrange multipliers to make higher-derivative gravity canonical is developed.