Scalar-assisted magnetogenesis during the radiation-dominated epoch

TL;DR

The paper tackles the origin of large-scale cosmic magnetic fields by proposing a RD-era magnetogenesis mechanism that avoids typical inflationary pitfalls. It introduces a U(1)-charged scalar φ with a nonzero VEV, coupled to a gauge field, along with an auxiliary χ that triggers a transient tachyonic growth of φ; this breaks conformal invariance and sources magnetic fields via scalar currents, while high conductivity suppresses electric-field production. A comprehensive Green’s-function formalism is developed to compute the magnetic power spectrum across epochs, including exact treatments before and after electron-positron annihilation and a detailed analysis of the tachyonic amplification’s impact on the scalar power spectrum. The main findings show that pre-annihilation magnetogenesis yields seeds too small to explain observations, but post-tachyonic amplification can generate seeds up to ~10^{-16} G on Mpc scales for reasonable choices of the model parameters, with the spectrum remaining subdominant in energy density and compatible with cosmological constraints. Overall, the work presents a self-consistent, minimal RD-era magnetogenesis scenario that circumvents the strong-coupling, backreaction, and baryon/isocurvature issues common in other proposals and offers a viable path to the observed cosmic magnetism.

Abstract

We propose a novel mechanism to generate primordial magnetic fields (PMFs) strong enough to explain the observed cosmic magnetic fields. We employ a scalar field charged under U(1) gauge symmetry with a non-trivial VEV to provide an effective mass term to the EM field and thus break its conformal invariance. The primordial magneto-genesis takes place in the radiation dominated (RD) epoch, after the electroweak symmetry breaking (EWSB) phase. As a result, our mechanism is naturally free from the over-production of electric fields due to high conductivity in the RD epoch, and the baryon isocurvature problem which takes place only if magneto-genesis happens before the ESWB phase. In addition, we find that a significant amount of PMFs can be generated when the scalar field experiences a tachyonic phase. In this case, the scalar field is light and weakly coupled and has negligible energy density compared to the cold dark matter, hence the strong coupling problem and the back-reaction problem are also absent. Therefore, our model is free from the above-mentioned problems that frequently appear in other primordial magneto-genesis scenarios.

Figures (3)

• Figure 1: The scalar power spectrum as a function of $k$. We take $\rho = 1.7 \times 10^{-26}$ and $m = 1.2 \times 10^{-30}$ [ GeV] for illustrative purpose such that the critical scale is $k_c = 5.9 \times 10^{25} \varrho {\rm Mpc}^{-1} \simeq 1 {\rm Mpc}^{-1}$.
• Figure 2: The momentum integral as a function of $k/k_c$. We demonstrate $\mathcal{I}_M$ for the range $k/k_c < 1$ in the left panel and $k/k_c \leq 2$ in the right panel. It is evident that $\mathcal{I}_M$ remains roughly a constant when $k/k_c \leq 0.1$ and quickly shrinks to 0 when $k/k_c > 0.1$.
• Figure 3: The magnetic power spectrum rescaled by $P_B(k=k_c)$.