Incompatibility of gravity theories with auxiliary fields with the Standard Model

TL;DR

Gravity theories with auxiliary fields, designed to modify Einstein's equations without adding new degrees of freedom, face significant issues as they induce deviations from the Standard Model unless parameters are tightly constrained, limiting their large-scale phenomenology.

Contribution

This paper demonstrates that auxiliary field gravity theories inherently cause deviations from the Standard Model, challenging their viability unless severely constrained.

Findings

Deviations from the Standard Model occur unless parameters are constrained.

Higher-order perturbations in Palatini $f({\cal R})$ gravity affect matter fields.

The issue is general for auxiliary field theories linked to surface singularities.

Abstract

Theories of gravity with auxiliary fields are of particular interest since they are able to circumvent Lovelock's theorem while avoiding to introduce new degrees of freedom. This type of theories introduces derivatives of the stress-energy tensor in the modified Einstein equation. This peculiar structure of the field equations was shown to lead to spacetime singularities on the surface of stars. Here we focus on yet another problem afflicting gravity theories with auxiliary field. We show that such theories introduce deviations to the Standard Model unless one severely constrains the parameters of the theory, preventing them to produce significant phenomenology at large scales. We first consider the specific case of Palatini $f({\cal R})$ gravity, to clarify the results previously obtained in arXiv:astro-ph/0308111. We show that the matter fields satisfy the Standard Model field equations which reduce to those predicted by General Relativity in the local frame only at tree level, whereas at higher orders in perturbation theory they are affected by corrections that percolate from the gravity sector regardless of the specific $f({\cal R})$ model considered. Finally, we show that this is a more general issue affecting theories with auxiliary fields connected to the same terms responsible for the appearance of surface singularities.