The role of vector fields in modified gravity scenarios

TL;DR

This paper systematically explores the role of gravitational vector fields in modified gravity models with specific symmetries, analyzing their impact on self-acceleration stability and fifth-force screening mechanisms.

Contribution

It provides a general framework for understanding how vector fields influence modified gravity phenomena under symmetry constraints, applicable to various models.

Findings

Vector fluctuations with vanishing kinetic terms cause instabilities.

Vector fields can significantly affect the Vainshtein screening radius.

Symmetry constraints limit the operators in the gravitational Lagrangian.

Abstract

Gravitational vector degrees of freedom typically arise in many examples of modified gravity models. We start to systematically explore their role in these scenarios, studying the effects of coupling gravitational vector and scalar degrees of freedom. We focus on set-ups that enjoy a Galilean symmetry in the scalar sector and an Abelian gauge symmetry in the vector sector. These symmetries, together with the requirement that the equations of motion contain at most two space-time derivatives, only allow for a small number of operators in the Lagrangian for the gravitational fields. We investigate the role of gravitational vector fields for two broad classes of phenomena that characterize modified gravity scenarios. The first is self-acceleration: we analyze in general terms the behavior of vector fluctuations around self-accelerating solutions, and show that vanishing kinetic terms of vector fluctuations lead to instabilities on cosmological backgrounds. The second phenomenon is the screening of long range fifth forces by means of Vainshtein mechanism. We show that if gravitational vector fields are appropriately coupled to a spherically symmetric source, they can play an important role for defining the features of the background solution and the scale of the Vainshtein radius. Our general results can be applied to any concrete model of modified gravity, whose low-energy vector and scalar degrees of freedom satisfy the symmetry requirements that we impose.