  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.
