Higher derivative and mimetic models on non flat FLRW space-times

TL;DR

This paper develops modified gravitational models inspired by Quantum Loop Cosmology for non-flat FLRW space-times, showing they can admit non-singular solutions, bounce metrics, or Big Bang singularities depending on the model and curvature.

Contribution

It introduces a class of non-analytic and mimetic gravitational models that yield second-order equations of motion in non-flat FLRW space-times, expanding the scope of effective Lagrangian approaches.

Findings

Some models admit non-singular solutions.

De Sitter space-time appears only in restricted models.

Models can produce bounce or Big Bang singular metrics.

Abstract

An effective Lagrangian approach, partly inspired by Quantum Loop Cosmology (QLC), is presented and formulated in a non flat FLRW space-times, making use of modified gravitational models. The models considered are non generic, and their choice is dictated by the necessity to have at least second order differential equations of motion in a non flat FLRW space-time. This is accomplished by a class of Lagrangian which are not analytic in the curvature invariants, or making use of a mimetic gravitational scalar field. It is shown that, for some effective models, the associated generalized Friedmann equation, in general, may admit non singular metrics as solutions, while the de Sitter space-time is present only for a restricted class, which includes General Relativity and Lovelock gravity. The other models admit pseudo de Sitter solutions, namely FLRW metrics, such that for vanishing spatial curvature looks like flat de Sitter patch, but for non vanishing spatial curvature are regular bounce metrics or, when the spatial curvature is negative, Big-Bang singular metrics.