N-flationary magnetic fields

TL;DR

Anber and Sorbo investigate the generation of cosmological magnetic fields during N-flation by coupling a multi-axion inflaton to a $U(1)$ gauge field. They combine the $N$ axions into an effective field $\Phi$ and show that the coupling $\Phi F_{\mu\nu}\tilde{F}^{\mu\nu}$ induces an instability with parameter $\xi=|\alpha\gamma|\sqrt{N\epsilon/2}$, amplifying magnetic fluctuations by $e^{\pi\xi}$ and producing maximally helical fields. The resulting magnetic energy can seed the dynamo through an inverse cascade, with coherence lengths growing after inflation; however, backreaction imposes bounds on $H$ and $\xi$, e.g. $H\lesssim 150\,\xi^{5/2}e^{-\pi\xi}M_P$, which translate to $\xi\lesssim 7$ under COBE normalization. The paper provides estimates for the present-day seed-field strength, $B_{\text{phys}}^f \sim 10^{-33}\,\frac{e^{\pi\xi}}{\xi^{17/12}}(T_{RH}/10^9\,\text{GeV})^{11/36}(l_{\text{phys}}/10\,\text{kpc})^{-9/4}\,\text{G}$, suggesting seeds in the range $10^{-30}$–$10^{-25}$ G are plausible for plausible $\xi$ and reheating temperatures. Overall, the work connects string-inspired inflation to cosmological magnetic fields via helicity-driven inverse cascade, while highlighting tight parameter constraints from backreaction.

Abstract

There is increasing interest in the role played by pseudo Nambu-Goldstone bosons (pNGBs) in the construction of string-inspired models of inflation. In these models the inflaton is expected to be coupled to gauge fields, and will lead to the generation of magnetic fields that can be of cosmological interest. We study the production of such fields mainly focusing on the model of N-flation, where the collective effect of several pNGBs drives inflation. Because the produced fields are maximally helical, inverse cascade processes in the primordial plasma increase significantly their coherence length. We discuss under what conditions inflation driven by pNGBs can account for the observed cosmological magnetic fields. A constraint on the parameters of this class of inflationary scenarios is also derived by requiring that the magnetic field does not backreact on the inflating background.