Non-Gaussian features of primordial magnetic fields in power-law inflation

We show that a conformal-invariance-violating coupling of the inflaton to electromagnetism produces a cross correlation between curvature fluctuations and a spectrum of primordial magnetic fields. According to this model, in the case of power-law inflation, a primordial magnetic field is generated with a nearly flat power spectrum and rms amplitude ranging from nG to pG. We study the cross correlation, a three-point function of the curvature perturbation, and two powers of the magnetic field, in real and momentum space. The cross-correlation coefficient, a dimensionless ratio of the three-point function with the curvature-perturbation and magnetic-field power spectra, can be several orders of magnitude larger than expected as based on the amplitude of scalar metric perturbations from inflation. In momentum space, the cross-correlation peaks for flattened triangle configurations, and is 3 orders of magnitude larger than the squeezed triangle configuration. These results suggest likely methods for distinguishing the observational signatures of the model.