On the primordial correlation of gravitons with gauge fields
  We calculate the primordial correlation of gravitons with an abelian gauge
field non-minimally coupled through a dynamical dilaton field or a volume
moduli during inflation in the early universe. In particular, we compute the
cross-correlation of a tensor mode with two gauge field modes and the
corresponding correlation functions for the associated magnetic and electric
fields using the in-in formalism. Moreover, using semi-classical methods, we
show that the three-point cross-correlation functions satisfy new consistency
relations (soft theorems) in the squeezed limit. Our findings exhibit a
complete agreement of the full in-in results with the new consistency
relations. An interesting consequence of our scenario is the possibility of a
novel correlation of the primordial tensor mode with the primordial curvature
perturbation induced by higher order quantum gravity corrections. The
anisotropic background created by long wavelength gauge field modes makes this
correlation function non-vanishing. Finally, we discuss how these three-point
correlation functions are imprinted on cosmological observables today and the
applications to scenarios of inflationary magnetogenesis.
