Cross-correlation between the curvature perturbations and magnetic fields in pure ultraslow roll inflation

Abstract

Motivated by the aim of producing significant number of primordial black holes, over the past few years, there has been a considerable interest in examining models of inflation involving a single, canonical field, that permit a brief period of ultraslow roll. Earlier, we had examined inflationary magnetogenesis— achieved by breaking the conformal invariance of the electromagnetic action through a coupling to the inflaton—in situations involving departures from slow roll. We had found that a transition from slow roll to ultraslow roll inflation can lead to a strong blue tilt in the spectrum of the magnetic field over small scales and also considerably suppress its strength over large scales. In this work, we consider the scenario of pure ultraslow roll inflation and show that scale invariant magnetic fields can be obtained in such situations with the aid of a nonconformal coupling function that depends on the kinetic energy of the inflaton. Apart from the power spectrum, an important probe of the primordial magnetic fields are the three-point functions, specifically, the cross-correlation between the curvature perturbations and the magnetic fields. We calculate the three-point cross-correlation between the curvature perturbations and the magnetic fields in pure ultraslow roll inflation for the new choice of the nonconformal coupling function. In particular, we examine the validity of the consistency condition that is expected to govern the three-point function in the squeezed limit and comment on the wider implications of the results we obtain.