A minimal set of invariants as a systematic approach to higher order gravity models

TL;DR

This paper introduces a systematic approach to higher-order gravity models using minimal sets of invariants, analyzing their dynamics and potential for cosmic acceleration.

Contribution

It proposes a novel method based on invariant theory to systematically construct and analyze higher-order gravity models for cosmology.

Findings

Models with accelerating attractors identified

Asymptotic behaviors analytically characterized

Connection established between invariants theory and cosmological models

Abstract

Higher-order gravity models have been recently the subject of much attention in the context of cosmic acceleration. These models are derived by adding various curvature invariants to the Einstein-Hilbert action. Several studies showed that these models can have late-time self-acceleration and could, in some cases, fit various observational constraints. In view of the infinite spectrum of invariants that could be built from curvature tensors, we propose here a method based on minimal sets of independent invariants as a possible route for a systematic approach to these models. We explore a connection made between theorems on bases in invariants theory in relativity and higher-order cosmological models. A dynamical system analysis is performed and some models with accelerating attractors are discussed. The asymptotic behavior of the models is also studied using analytical calculations.