Anisotropic deformations in a class of projectively-invariant metric-affine theories of gravity

TL;DR

This paper investigates how certain gravity theories with projective symmetry can exhibit anisotropic deformations even with isotropic matter, revealing limitations and pathological behaviors in these models.

Contribution

It demonstrates that in projectively-invariant metric-affine theories, the deformation matrix can be anisotropic despite isotropic sources, and identifies issues with anisotropic solutions.

Findings

Eddington-inspired-Born-Infeld theories do not allow anisotropic deformations.

More general theories permit anisotropic deformations.

Anisotropic solutions often exhibit pathological physical behavior.

Abstract

Among the general class of metric-affine theories of gravity, there is a special class conformed by those endowed with a projective symmetry. Perhaps the simplest manner to realise this symmetry is by constructing the action in terms of the symmetric part of the Ricci tensor. In these theories, the connection can be solved algebraically in terms of a metric that relates to the spacetime metric by means of the so-called deformation matrix that is given in terms of the matter fields. In most phenomenological applications, this deformation matrix is assumed to inherit the symmetries of the matter sector so that in the presence of an isotropic energy-momentum tensor, it respects isotropy. In this work we discuss this condition and, in particular, we show how the deformation matrix can be anisotropic even in the presence of isotropic sources due to the non-linear nature of the equations. Remarkably, we find that Eddington-inspired-Born-Infeld theories do not admit anisotropic deformations, but more general theories do. However, we find that the anisotropic branches of solutions are generally prone to a pathological physical behaviour.