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Higher-order gravity models have been recently the subject of much attentionin the context of cosmic acceleration. These models are derived by addingvarious curvature invariants to the Einstein-Hilbert action. Several studiesshowed that these models can have late-time self-acceleration and could, insome cases, fit various observational constraints. In view of the infinitespectrum of invariants that could be built from curvature tensors, we proposehere a method based on minimal sets of independent invariants as a possibleroute for a systematic approach to these models. We explore a connection madebetween theorems on bases in invariants theory in relativity and higher-ordercosmological models. A dynamical system analysis is performed and some modelswith accelerating attractors are discussed. The asymptotic behavior of themodels is also studied using analytical calculations.

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