Correspondence between modified gravity and general relativity with scalar fields

Abstract

We describe a novel procedure to map the field equations of nonlinear Ricci-based metric-affine theories of gravity, coupled to scalar matter described by a given Lagrangian, into the field equations of General Relativity coupled to a different scalar field Lagrangian. Our analysis considers examples with a single and N real scalar fields, described either by canonical Lagrangians or by generalized functions of the kinetic and potential terms. In particular, we consider several explicit examples involving f (R) theories and the Eddington-inspired Born-Infeld gravity model, coupled to different scalar field Lagrangians. We show how the nonlinearities of the gravitational sector of these theories can be traded to nonlinearities in the matter fields, and how the procedure allows to find new solutions on both sides of the correspondence. The potential of this procedure for applications of scalar field models in astrophysiftcal and cosmological scenarios is highlighted. *

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

“…At this point it is important to note that according to (5), the Ricci tensor R µν (Γ) and all its possible scalar contractions with g αβ can be algebraically related to T µ ν . As a result, the matrix Ω turns out to be a function of T µ ν , which implies that the relation between q µν and g µν defined in (13) will be highly nonlinear in general.…”

“…Given this result, the tensor structures that appear in the expansion (17) of the deformation matrix are δ µ ν and powers of K µ ν . The setting is very closely related to the case where the matter sector is described by scalar fields [5], where arbitrary powers of K µ ν turn out to be linear combinations of the identity and K µ ν so that the correspondence between RBGs and GR can be explicitly unveiled.…”

“…In this work we continue a program initiated in [4] in which the field equations of Ricci-Based Gravity theories (RBGs) coupled to standard matter are put into correspondence with the field equations of GR coupled to the same matter species but with a different, typically nonlinear Lagrangian. In [5] the focus was on the case of scalar fields and the non-perturbative results obtained there were used to generate new solutions in nonlinear RBG theories starting with known solutions in GR [6]. In [7] the equivalence between (linear or nonlinear) electric fields and anisotropic fluids was exploited in a similar fashion.…”

“…To clarify this point and set the path to explore more general electromagnetic effects in nonlinear RBGs, it is necessary to extend the analysis of [7] to the complete electromagnetic case. Paralleling the approach of [5] for scalar fields, here we extend the correspondence between GR and RBGs for arbitrary (linear and nonlinear) electromagnetic fields. Our results confirm that a correspondence for electromagnetic fields also exists, and recovers the electric case in the appropriate limit.…”

A generalized Weyl structure with arbitrary non-metricity

“…Once understood that disformal generalizations of a Weyl structure necessarily lead to abandoning the vectorial non-metricity postulate, let us consider two possible kinds of such generalizations: one relying on GL (N, R) as the symmetry group, and another kind of deformations which are present in the so-called Ricci-Based Gravity theories (RBGs), a broad class of metric-affine theories with projective symmetry recently considered in the literature [33,34,[50][51][52][53][54].…”