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

15 pages, 4 figures, matches JCAP accepted version

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• Dynamical systems applied to cosmology: dark energy and modified gravity
• Testing General Relativity in Cosmology
• On the co-existence of matter dominated and accelerating solutions in f(G)-gravity
• Covariant equations of motion for test bodies in gravitational theories with general nonminimal coupling
• Conservation laws in gravitational theories with general nonminimal coupling
• Lessons from $f(R,R_c^2,R_m^2,L_m)$ gravity: Smooth Gauss-Bonnet limit, energy-momentum conservation and nonminimal coupling
• Supernova, baryon acoustic oscillations, and CMB surface distance constraints on f(G) higher order gravity models
• A minimal set of invariants as a systematic approach to higher order gravity models: Physical and Cosmological Constraints
• Is the use of Christoffel connection in gravity theories conceptually correct?
• On energy-momentum tensor for gravitational waves in $f(R)$ gravity