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 astrophysical and cosmological scenarios is highlighted.
Highlights
In the wake of gravitational wave astronomy after the observation of binary black hole [1, 2] and neutron star mergers [3] by the LIGO/Virgo Collaboration, and the future launching of new cosmological probes such as EUCLID [4, 5], many of the gravitational extensions of General Relativity (GR) proposed in the literature will be put to experimental test in astrophysical [6, 7], extragalactic [8] and cosmological [9] contexts, going beyond the classical solar system ones [10]
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
In this work we have investigated a family of metricaffine theories of gravity whose Lagrangian density is a non-linear function of scalars built out of contractions of the metric and the Ricci tensor (Ricci-Based Gravity theories or Ricci-based gravities (RBGs)), and coupled to scalar field matter
Summary
In the wake of gravitational wave astronomy after the observation of binary black hole [1, 2] and neutron star mergers [3] by the LIGO/Virgo Collaboration, and the future launching of new cosmological probes such as EUCLID [4, 5], many of the gravitational extensions of General Relativity (GR) proposed in the literature will be put to experimental test in astrophysical [6, 7], extragalactic [8] and cosmological [9] contexts, going beyond the classical solar system ones [10]. The fact that gμν cannot always be explicitly expressed in terms of qμν and the matter fields is an important drawback, as it forces one to deal with cumbersome equations and rely on the existence of the particular simplifications that may arise in scenarios with specific symmetries This is the case, for instance, of homogeneous and isotropic cosmological models [29, 30], and of static spherically symmetric spacetimes [31,32,33]. The map between theories that we present here proposes the reinterpretation of the terms on the right-handside of the Einstein frame metric field equations in such a way that they take on the same structure as the stressenergy tensor of a nonlinear matter field This identification is subject to certain integrability conditions, related to stress-energy conservation, between the effective Lagrangian and its partial derivatives, which involve both the metric field equations and the scalar field ones.
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