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 EinsteinHilbert 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.PACS numbers: 98.80.-k, 95.36.+x

Lessons fromf(R,Rc2,Rm2,Lm)gravity: Smoot

“…which is consistent with the field equation in [22]. Thus, for a Lagrangian density dependent on the traceless…”

A minimal set of invariants as a systematic approach to higher order gravity models: physical and cosmological constraints

“…The method is based on a connection made between theorems in invariants theory in relativity and higher-order cosmological models. We outline here the major ideas of this method and refer the reader to [4] for the detail. The method involves the identification of the Petrov type corresponding to the symmetry of the spacetime, e.g.…”

“…The corresponding dynamics allows for some models to have late-time self-acceleration without the need for a cosmological constant or other forms of dark energy. In previous work [4], the authors were able to show a range of these models in the basis {R, R1} that showed self-acceleration at late times using numerical and analytical methods. The discussion there focused on power-law type solutions with late-time acceleration free from separatrix singularities, so that the models can transition from a matter dominated phase to the desired cosmic acceleration phase seen by current observations.…”

“…Next, to build models that avoid the separatrix, we choose to set a 1 = a 3 which avoids the singularity atä = 0 [4]. From now on, we limit the discussion to the case a 1 = a 3 = 1, and actions of the form…”

“…Now, we consider power-law solutions with a(t) ∝ t p in flat FLRW spacetime for our accelerating branch as derived in our previous work [4] and as given further by the solutions (14). For radiation dominated and matter dominated decelerating phases, we use p = 1/2 and p = 2/3, respectively.…”