Cross-correlations between scalar perturbations and magnetic fields in
  bouncing universes
  Bouncing scenarios offer an alternative to the inflationary paradigm for the
generation of perturbations in the early universe. Recently, there has been a
surge in interest in examining the issue of primordial magnetogenesis in the
context of bouncing universes. As in the case of inflation, the conformal
invariance of the electromagnetic action needs to be broken in bouncing
scenarios in order to generate primordial magnetic fields which correspond to
observed strengths today. The non-minimal coupling, which typically depends on
a scalar field that possibly drives the homogeneous background, leads to a
cross-correlation at the level of the three-point function between the
perturbation in the scalar field and the magnetic fields. This has been studied
in some detail in the context of inflation and, specifically, it has been
established that the three-point function satisfies the so-called consistency
relation in the squeezed limit. In this work, we study the cross-correlation
between the magnetic fields and the perturbation in an auxiliary scalar field
in a certain class of bouncing scenarios. We consider couplings that lead to
scale invariant spectra of the magnetic field and evaluate the corresponding
cross-correlation between the magnetic field and the perturbation in the scalar
field. We find that, when compared to de Sitter inflation, the dimensionless
non-Gaussianity parameter that characterizes the amplitude of the
cross-correlations proves to be considerably larger in bouncing scenarios. We
also show that the aforementioned consistency condition governing the
cross-correlation is violated in the bouncing models. We discuss the
implications of our results.
