Dynamics of a Homogeneous and Isotropic Space in Pure Cubic f(R) Gravity

Polina Petriakova

doi:10.3390/physics3020027

Abstract

The possible ways of dynamics of a homogeneous and isotropic space described by the Friedmann–Lemaitre–Robertson–Walker metric in the framework of cubic in the Ricci scalar f(R) gravity in the absence of matter are considered. This paper points towards an effective method for limiting the parameters of extended gravity models. A method for f(R)-gravity models, based on the metric dynamics of various model parameters in the simplest example is proposed. The influence of the parameters and initial conditions on further dynamics are discussed. The parameters can be limited by (i) slow growth of space, (ii) instability and (iii) divergence with the inflationary scenario.

Highlights

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One of the simplest approaches to modified gravity is f ( R) gravity, with f ( R) being function of the Ricci scalar R. This class of theories is widely used in modern research [11,12,13,14] and, in some cases, successfully solves particular problems and fits the observational cosmology data [15,16,17,18]
After the damping of the oscillations of the corresponding quantities, a transitional regime begins to the general relativity (GR)

Summary

Introduction

One of the simplest approaches to modified gravity is f ( R) gravity, with f ( R) being function of the Ricci scalar R This class of theories is widely used in modern research [11,12,13,14] and, in some cases, successfully solves particular problems and fits the observational cosmology data [15,16,17,18]. The Starobinsky’s inflationary model is a particular solution to the class of theories of gravity with higher derivatives, which are devoid of ghost degrees of freedom, perturbatively unitary and finite at the quantum level [20] This model has a “graceful exit” from inflation and provides a mechanism for the subsequent creation and final thermalization of the standard matter.

Basic Equations

Analysis in the Einstein Frame

Numerical Results

Discussion