Thermal enhancement of inflationary magnetic fields

Abstract

We investigate primordial magnetogenesis by assuming the gauge field is prepared in a thermal state during inflation rather than the standard Bunch-Davies vacuum. The temperature $\mathcal{T}$ introduces a physical scale that breaks conformal invariance at the level of the state while preserving the standard Maxwell action. This modification results in a {\it dissipative boost} that alters the magnetic energy density scaling from $a^{-4}$ to $a^{-3}$, resulting in a present-day magnetic field $B_0$ enhancement that can potentially range from about $10^{8}$ to $10^{16}$ on galactic scales. While this toy model alone does not satisfy observational lower bounds, it demonstrates that thermal initial conditions can significantly mitigate the conformal obstruction. Our results suggest that embedding this mechanism within a fully dynamical warm inflation framework, where dissipation continuously maintains the thermal bath, provides a highly promising path towards successfully realizing a minimal model of inflationary magnetogenesis without the need to invoke non-minimal couplings, anomalous background dynamics or nonlinear extensions of electrodynamics.

Figures (1)

• Figure 1: Thermal correction factor $\coth(\frac{k}{2a\mathcal{T}})$ compared with the Rayleigh-Jeans approximation of the full curve is plotted as a function of the dimensionless ratio $\log_{10}\frac{k_c^*}{k_c}$. $\lambda^*_c=\frac{2\pi a}{k_c^*}$ is the pivot scale introduced satisfying $k_c^*/a\sim 2\mathcal{T}$. The temperature here is chosen to be $\mathcal{T}=10^{10}\rm GeV$ for a specific illustration. It is clear that at scales of astrophysical and cosmological interest which are significantly larger than the pivot scale $\sim 10^{-49}\rm Mpc$, the amplification factor is extremely well approximated.