Magnetogenesis and the primordial non-gaussianity

Abstract

The primordial density fluctuation inevitably couples to all forms of matter via loop corrections and depends on the ambient conditions while inflation was ongoing. This gives us an opportunity to observe processes which were in progress while the universe was inflating, provided they were sufficiently dramatic to overcome suppression by powers of (H/MP)^2 ~ 10^(-9), where H is the Hubble scale during inflation and MP is the Planck mass. As an example, if a primordial magnetic field was synthesized during inflation, as suggested by some interpretations of the apparently universal 10^(-6) gauss field observed on galactic scales, then this could leave traces in inflationary observables. In this paper, I compute corrections to the spectrum and bispectrum generated by a varying electromagnetic coupling during inflation, assuming that the variation in this coupling is mediated by interaction with a collection of light scalar fields. If the mass scale associated with this interaction is too far below the Planck scale then the stability of perturbation theory can be upset. For the mass-scale which is relevant in the standard magnetogenesis scenario, however, the theory is stable and the model is apparently consistent with observational constraints.

Figures (3)

• Figure 1: Schwinger-formalism diagrams for the loop correction to the scalar two-point function which arise from mixing with gauge bosons. Straight lines indicate scalar quanta, which only appear on the external legs. The interior loop, composed of wavy lines, indicates mixing with virtual quanta borrowed from the ambient electric and magnetic fields. The fields associated with external legs are always of $+$ type, whereas the vertices can be of $+$ or $-$ type. The $(+,+)$ and $(-,-)$ diagrams form one complex conjugate pair, and the $(+,-)$ and $(-,+)$ diagrams form another.
• Figure 2: Diagrams contributing to the three-point scalar expectation value. As before, straight lines (appearing on the external legs of the diagrams) indicate scalar quanta), whereas wavy lines indicate virtual gauge bosons circulating the the loop. These diagrams break into four groups of complex conjugate pairs, with the $(+,+,+)$ and $(-,-,-)$ diagrams forming one pair and the permutations of the $(+,+,-)$ and $(-,-,+)$ diagrams forming the other three groups.
• Figure 3: All-scalar loop correction from the $V"'$ vertex, common to all scalar field models of inflation.