The Effective Field Theory of Vector-Tensor Theories

TL;DR

This paper develops an effective field theory framework for vector-tensor theories of dark energy, highlighting their unique symmetry breaking patterns and providing tools to analyze their cosmological perturbations and observational signatures.

Contribution

It introduces a systematic EFT formulation for vector-tensor theories, distinguishing them from scalar-tensor theories and analyzing their linear cosmological perturbations.

Findings

Unified EFT description of vector-tensor theories

Identification of phenomenological functions and consistency relations

Calculation of effective gravitational coupling and slip parameter

Abstract

We investigate a systematic formulation of vector-tensor theories based on the effective field theory (EFT) approach. The input of our EFT is that the spacetime symmetry is spontaneously broken by the existence of a preferred timelike direction in accordance with the cosmological principle. After clarifying the difference of the symmetry breaking pattern from the conventional EFT of inflation/dark energy, we find an EFT description of vector-tensor theories around the cosmological background. This approach not only serves as a unified description of vector-tensor theories but also highlights universal differences between the scalar-tensor theories and the vector-tensor theories. The theories having different symmetry breaking patterns are distinguished by a phenomenological function and consistency relations between the EFT coefficients. We study the linear cosmological perturbations within our EFT framework and discuss the characteristic properties of the vector-tensor theories in the context of dark energy. In particular, we compute the effective gravitational coupling and the slip parameter for the matter density contrast in terms of the EFT coefficients.