Fluctuations of inflationary magnetogenesis
  This analysis aims at exploring what can be said about the growth rate of
magnetized inhomogeneities under two concurrent hypotheses: a phase of quasi-de
Sitter dynamics driven by a single inflaton field and the simultaneous presence
of a spectator field coupled to gravity and to the gauge sector. Instead of
invoking ad hoc correlations between the various components, the system of
scalar inhomogeneities is diagonalized in terms of two gauge-invariant
quasi-normal modes whose weighted sum gives the curvature perturbations on
comoving orthogonal hypersurfaces. The predominance of the conventional
adiabatic scalar mode implies that the growth rate of magnetized
inhomogeneities must not exceed 2.2 in Hubble units if the conventional
inflationary phase is to last about 70 efolds and for a range of slow roll
parameters between 0.1 and 0.001. Longer and shorter durations of the quasi-de
Sitter stage lead, respectively, either to tighter or to looser bounds which
are anyway more constraining than the standard backreaction demands imposed on
the gauge sector. Since a critical growth rate of order 2 leads to a quasi-flat
magnetic energy spectrum, the upper bounds on the growth rate imply a lower
bound on the magnetic spectral index. The advantages of the uniform curvature
gauge are emphasized and specifically exploited throughout the treatment of the
multicomponent system characterizing this class of problems.
