Fluctuations of inflationary magnetogenesis

Abstract

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.Comment: 37 pages, 4 figure

Primordial magnetic fields from the post-inflationary universe

“…In other words, the electromagnetic vector potential during inflation is required to possess a large time-derivative, and therefore leads to excessive production of electric fields. Recently it has also been pointed out that the generated electromagnetic fields can induce cosmological density perturbations beyond the observed value, and works [23,24,25,26,27] have imposed further constraints on inflationary magnetogenesis. (See also [28,29,30,31] and references therein for constraints on primordial magnetic fields from CMB and large-scale structure data.)…”

Probing large-scale magnetism with the cosmic microwave background

“…where R is the curvature perturbation on comoving orthogonal hypersurfaces defined in Eq. (2.46); Σ R contains the contribution of the electromagnetic fields, of the non-adiabatic pressure fluctuations and of the total anisotropic stress: [70] and subsequently applied to various problems [144] involving the inflationary initial conditions of the magnetized curvature perturbations. When δp nad → 0, Π tot → 0 and in the absence of electromagnetic contributions, Eq.…”

“…(2.45). The continuity of the magnetized perturbations across the inflationary transition has been analyzed in terms of these variables and the related temperature and polarization anisotropies have been computed in [70,144].…”

“…While it would superficially seem that the inflationary contributions simply renormalize the standard adiabatic mode, the new terms in Eq. (3.69) should be used to set joined bounds on the magnetic field intensity, on the total number of efolds [70] (see also [143]) or even on the tensor to scalar ratio when, for instance, the inflaton is directly coupled to the gauge fields. Note finally that in the models of inflationary magnetogenesis the inflaton might not be directly coupled to the gauge fields but to one (or more) spectator fields.…”

Constraints on primordial magnetic fields from inflation

“…(3.10). Here we should remark that this condition is not sufficient when taking into account the cosmological perturbations, as the vector field itself sources curvature perturbations of roughly [19][20][21][22][23] …”