Ricci-Based Gravity theories and their impact on Maxwell and nonlinear electromagnetic models

Abstract

We extend the correspondence between metric-affine Ricci-Based Gravity theories and General Relativity (GR) to the case in which the matter sector is represented by linear and nonlinear electromagnetic fields. This complements previous studies focused on fluids and scalar fields. We establish the general algorithm that relates the matter fields in the GR and RBG frames and consider some applications. In particular, we find that the so-called Eddington-inspired Born-Infeld gravity theory coupled to Maxwell electromagnetism is in direct correspondence with GR coupled to Born-Infeld electromagnetism. We comment on the potential phenomenological implications of this relation.

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.…”

“…δg μν is the usual energy-momentum tensor of the matter sector and we have introduced the object √ −qq μν ≡ √ −g ∂ F ∂R μν . In the usual treatment of RBGs, projective symmetry is assumed, which from (20) restricts the dependence of the action only to the symmetric part of the Ricci tensor. Here, we want to offer a more detailed discussion about what are the consequences of breaking the projective symmetry in RBGs than that presented in [14].…”

“…[27][28][29][30][31]). As a matter of fact, starting from a standard canonical scalar field and usual Maxwellian electrodynamics in the RBG frame, the Einstein frame formulation will precisely be K -essence [18] and non-linear electrodynamics respectively [20].…”

Conformally invariant proper time with general non-metricity

“…While the consequences of torsion have been fairly analyzed up to date, those of non-metricity have not yet been fully explored. Several classes of theories which feature torsion and/or non-metricity that have been studied in the literature are gauge theories of gravity [7][8][9], Ricci-Based gravity theories (which encompass Palatini f (R) or Born-Infeld gravity for instance) [10][11][12][13][14][15][16][17][18], teleparallel and symmetric teleparallel [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], hybrid gravity [36], Palatini scalar-tensor theories [37], infinite derivative theories, etc. [38].…”

Quintessential Inflation with Dynamical Higgs Generation as an Affine Gravity

“…It has attracted since then a significant interest primarily due to the established dynamical equivalence [106] of the three principal formulations of standard Einstein's gravity -purely metric (second-order formalism), metric-affine (Palatini or first-order formalism) and purely affine formalism. For a more recent developments and list of references, see [107][108][109][110][111][112][113][114][115][116][117][118][119][120][121][122][123], in particular about incorporating torsion and explaining dark energy as an instrinsic property of space-time.…”