General approach to the Lagrangian ambiguity in f(R,\xa0T) gravity

G A Carvalho,H O Oliveira,R V Lobato,F Rocha

doi:10.1140/epjc/s10052-021-08920-4

Abstract

The f(R, T) gravity is a theory whose gravitational action depends arbitrarily on the Ricci scalar, R, and the trace of the stress–energy tensor, T; its field equations also depend on matter Lagrangian, mathscr {L}_{m}. In the modified theories of gravity where field equations depend on Lagrangian, there is no uniqueness on the Lagrangian definition and the dynamics of the gravitational and matter fields can be different depending on the choice performed. In this work, we have eliminated the mathscr {L}_{m} dependence from f(R, T) gravity field equations by generalizing the approach of Moraes in Ref. [1]. We also propose a general approach where we argue that the trace of the energy–momentum tensor must be considered an “unknown” variable of the field equations. The trace can only depend on fundamental constants and few inputs from the standard model. Our proposal resolves two limitations: first the energy–momentum tensor of the f(R, T) gravity is not the perfect fluid one; second, the Lagrangian is not well-defined. As a test of our approach we applied it to the study of the matter era in cosmology, and the theory can successfully describe a transition between a decelerated Universe to an accelerated one without the need for dark energy.

Highlights

General Relativity (GR) is one of the cornerstones of modern physics being stated as the standard model of gravitation and cosmology
Combined data from Cosmic Microwave Background Radiation (CMB) [2] and from Baryonic Acoustic Oscillaa e-mail: geanderson.araujo.carvalho@gmail.com author) b e-mail: rocha.pereira.flavia@gmail.com c e-mail: ronaldo.lobato@tamuc.edu (corresponding tions (BAO), indicate that the Universe is spatially flat, it is in accelerated expansion [3,4], and it is composed of 96% of unknown matter-energy, commonly known as dark matter and dark energy, respectively
This article is organized as follows: Sect. 2 presents a basic overview on general properties of the f (R, T ) gravity, in Sect. 3 we derive the traceless field equations for a generic f (R, T ) functional, in Sect. 4 we present a consistent approach for the Lagrangian ambiguity choice, in Sect. 5 we apply the theory to describe the matter era of cosmology and show that a transition between a decelerated Universe to an accelerated one is possible in f (R, T ) cosmology and in Sect. 6 we conclude and discuss possible applications of the theory presented here

Summary

Introduction

General Relativity (GR) is one of the cornerstones of modern physics being stated as the standard model of gravitation and cosmology. As pointed by [13], a more rich phenomenology could arise from a non-minimal geometry-matter coupling, what is within the motivations behind the present work This new general approach eliminates the Lagrangian ambiguity choice. The gravitational field equations involve only traceless parts of the Riemann/energy–momentum tensor Nowadays, this formulation was reborn as “unimodular gravity”, due to a fixation on the metric determinant detgμν ≡ g = 1, and it is applied to solve the problem of the discrepancy between the vacuum energy density and the observed value of the cosmological constant [16,17,18,19,20]. We will use it in a more consistent approach to the Lagrangian ambiguity issue in f (R, T ) gravity

A more consistent approach to the Lagrangian ambiguity choice

Cosmology in the general approach for the Lagrangian ambiguity

Findings

Discussion