Effective interactions in Ricci-Based Gravity below the non-metricity scale

Abstract

We show how minimally-coupled matter fields of arbitrary spin, when coupled to Ricci-Based Gravity theories, develop non-trivial effective interactions that can be treated perturbatively only below a characteristic high-energy scale ΛQ. Our results generalize to arbitrary matter fields those recently obtained for spin 1/2 fields in [1]. We then use this interactions to set bounds on the high-energy scale ΛQ that controls departures of Ricci-Based Gravity theories from General Relativity. Particularly, for Eddington-inspired Born-Infeld gravity we obtain the strong bound |κ| < 10 −26 m 5 kg −1 s −2 . PACS numbers: arXiv:1907.05615v1 [hep-th] 12 Jul 2019 3 With the well known exception of Lovelock theories [65]. 4 Known as Einstein-Cartan-Sciamma-Kibble or ECKS theory. 5 If one considers coupling spinors to GR this is not strictly true, since there arise torsion corrections sourced by spin-density. 6 In fact, the class of RBG theories, which contains f (R) theories, can be defined as the most general class of theories with projective symmetry and whose Lagrangian is given by an analytic scalar function of the metric and the Ricci tensor.

New class of ghost- and tachyon-free metric affine gravities

“…In the literature, more attention has been given to theories with torsion, but recently there has been a great deal of interest for MAGs with non-metricity, see e.g. [3][4][5][6][7][8][9][10][11][12].…”

Metric-affine bumblebee gravity: classical aspects

“…Newtonian and post-Newtonian corrections) are negligible. As a result, particle physics experiments can be used to place strong constraints on the parameters of those gravity models [35,36].…”

Instabilities in metric-affine theories of gravity with higher order curvature terms

“…Since our purpose here is showing the (generically) pathological nature of higher order curvature theories of gravity in the metric-affine formalism, we simply take these theories as a benchmark to illustrate the potential problems suffered by metric-affine theories. It is important however to stress that RBG theories have received considerable attention in the literature [5,[16][17][18][19][20][21][22], due to their interesting properties that make them appealing and more tractable than other more general metric-affine theories, thus being useful as a proxy to better understanding general metric-affine theories.…”

“…This energy-momentum is highly non-linearly related to T μν [17], and will feature new interactions between all the matter fields in general [21,22], which are the origin of the different phenomenology and solutions that differ from the usual GR behaviour. Let us stress however that these theories are nothing but standard GR in disguise.…”

“…The peculiar property of the RBG with projective symmetry is that the interactions in the matter sector present a somewhat universal form (that of course depends on the specific theory, i.e., the function F). As we have discussed above, if we start from minimally coupled matter fields, all the new interactions will be generated through the total energy-momentum tensor [17,22]. Assuming that the most relevant interactions in the gravitational sector of RBG appear at some specific scale , which means that the function F only contains one additional dimensionfull parameter, then all the new interactions in the matter sector will not only be universally constructed in terms of T μν , but they all will in turn have the same coupling constant.…”