Vector disformal transformation of cosmological perturbations

TL;DR

This paper investigates how vector disformal transformations affect cosmological perturbations, revealing that certain transformations can alter gravitational waves and curvature perturbations, with potential observational implications for early universe cosmology.

Contribution

It classifies three types of vector disformal transformations and analyzes their effects on cosmological perturbations, highlighting observable differences in gravitational waves and curvature.

Findings

Type (i) transformations do not change curvature or gravitational waves.

Type (ii) transformations change gravitational waves but not curvature.

Type (iii) transformations alter both curvature and gravitational waves.

Abstract

We study disformal transformations of cosmological perturbations by vector fields in theories invariant under U(1) gauge transformations. Three types of vector disformal transformations are considered: (i) disformal transformations by a single timelike vector; (ii) disformal transformations by a single spacelike vector; and (iii) disformal transformations by three spacelike vectors. We show that transformations of type (i) do not change either curvature perturbation or gravitational waves; that those of type (ii) do not change curvature perturbation but change gravitational waves; and that those of type (iii) change both curvature perturbation and gravitational waves. Therefore, coupling matter fields to the metric after disformal transformations of type (ii) or (iii) in principle have observable consequences. While the recent multi-messenger observation of binary neutron stars has singled out a proper disformal frame at the present epoch with a high precision, the result of the present paper may thus help distinguishing disformal frames in the early universe.