Accelerated Cosmological Models in First-Order Non-Linear Gravity

TL;DR

This paper explores modified gravity theories based on functions of the Ricci scalar to explain the universe's acceleration without dark energy, analyzing their cosmological implications and proposing a new Lagrangian form.

Contribution

It investigates alternative gravitational models in the Palatini formalism, providing solutions and proposing a novel Lagrangian to account for cosmic acceleration.

Findings

Theories can explain universe acceleration and inflation without dark energy.

Palatini formalism avoids instability issues in these models.

A new Lagrangian involving inverse sinh(R) is proposed for cosmic acceleration.

Abstract

The evidence of the acceleration of universe at present time has lead to investigate modified theories of gravity and alternative theories of gravity, which are able to explain acceleration from a theoretical viewpoint without the need of introducing dark energy. In this paper we study alternative gravitational theories defined by Lagrangians which depend on general functions of the Ricci scalar invariant in minimal interaction with matter, in view of their possible cosmological applications. Structural equations for the spacetimes described by such theories are solved and the corresponding field equations are investigated in the Palatini formalism, which prevents instability problems. Particular examples of these theories are also shown to provide, under suitable hypotheses, a coherent theoretical explanation of earlier results concerning the present acceleration of the universe and cosmological inflation. We suggest moreover a new possible Lagrangian, depending on the inverse of sinh(R), which gives an explanation to the present acceleration of the universe.