Vector disformal transformation of cosmological perturbations

Understand

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.