Modified Gravity Models Admitting Second Order Equations of Motion

TL;DR

This paper explores higher order geometric modifications to Einstein's gravity that still produce second order equations of motion, using the metric formalism and considering specific space-times.

Contribution

It introduces a systematic approach to identify all possible invariant scalars leading to second order equations in modified gravity models.

Findings

Identifies all invariant scalars that yield second order equations.

Analyzes polynomial and non-polynomial gravity theories.

Provides a framework for constructing viable modified gravity models.

Abstract

The aim of this paper is to find higher order geometrical corrections to the Einstein-Hilbert action that can lead to only second order equations of motion. The metric formalism is used, and static spherically symmetric and Friedmann-Lema\^itre space-times are considered, in four dimensions. The FKWC-basis are introduced in order to consider all the possible invariant scalars, and both polynomial and non-polynomial gravities are investigated.