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.
Highlights
Inflation is arguably the most promising scenario of the early universe, by which various conceptual issues in the standard big-bang cosmology can be addressed
The tensor perturbations hij are invariant in the timelike case, while we saw that they are not when we consider 3 spacelike vectors. This is due to the fact that, unlike the case we considered the single timelike vector does not introduce any tensor perturbation with which gravitational waves may mix
In this work we have studied disformal transformation in models containing a complex scalar field which is charged under a Uð1Þ gauge field
Summary
Inflation is arguably the most promising scenario of the early universe, by which various conceptual issues in the standard big-bang cosmology can be addressed. One might hope that cosmological perturbation might be a probe of disformal frame in the early universe, especially during inflation, since it is cosmological perturbation that connects theoretical predictions of inflationary models with observations For this reason, many authors have investigated disformal transformations of the spacetime metric by a scalar field [5,6,7,8,9,10,11,12]. This is well-motivated as in theories of high energy physics and particle physics vector fields ( gauge fields) play important roles so one naturally expects that they may play important roles during inflation as well In those models, vector fields may participate in the disformal transformation between the original metric and the effective metric.
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