Parametric Resonance and Backreaction Effects in Magnetogenesis from Ultralight Dark Matter

TL;DR

This work investigates magnetogenesis from ultralight dark matter φ coupled to electromagnetism via an axion-like term, focusing on a previously neglected narrow-band parametric resonance channel in addition to the tachyonic channel. Using Mathieu-equation analysis and Floquet theory, they derive the narrow-band Floquet exponent $\mu_p = \tfrac{1}{4} g_{\phi\gamma} m \Phi$ and identify the conditions under which the narrow resonance can dominate (notably when $\tilde{g}_{\phi\gamma}<10^{-9}$). Backreaction analyses—both energetic and coherence-based—suggest that a fraction $F$ of order unity of the initial dark-matter energy can be transferred to gauge fields before the resonance terminates, indicating robustness of the mechanism; numerical studies corroborate the analytic picture, showing tachyonic dominance at strong coupling and narrow-band dominance at weak coupling. Overall, the paper strengthens the plausibility of late-time magnetogenesis by ultralight dark matter and connects the mechanism to gauge preheating literature, with implications for the generation of cosmological magnetic fields on megaparsec scales.

Abstract

We take a more detailed look at the recently proposed magnetogenesis mechanism triggered by ultralight dark matter coupled to electromagnetism. The proposed mechanism made use of a tachyonic resonance channel which leads to the exponential amplification of infrared modes. Here, we first investigate a possible narrow band parametric resonance channel which can produce photons at higher frequencies. Secondly, we estimate the effects of back-reaction on terminating the resonance. We find that there is indeed a narrow resonance channel. It is characterized by a Floquet exponent which is slightly smaller than the corresponding exponent for the tachyonic resonance. However, there is a region of parameter space (corresponding to a very small coupling constant) for which the tachyonic resonance is ineffective. In this case, the narrow resonance will dominate, and it will still be sufficiently strong to generate the observed magnetic fields on cosmological scales. Our analytical treatment of the back-reaction effects considered here indicates that a fraction of order one of the initial dark matter density can flow into the gauge fields. Hence, our magnetogenesis scenario appears to be robust to back-reaction effects.

Figures (3)

• Figure 1: Evolution of the gauge field mode $A_k$ and the background scalar field in the case of large coupling (${\tilde{g_{\phi \gamma}}} = 5 \times 10^2$ - see text for description of the curves), and for $k_T = 0.5k_c$.
• Figure 2: Evolution of the gauge field mode $A_k$ and the background scalar field in the case of large coupling (${\tilde{g_{\phi \gamma}}} = 5 \times 10^2$ - see text for description of the curves), and for $k_T = 0.1k_c$.
• Figure 3: Evolution of the gauge field mode $A_k$ and the background scalar field in the case of small coupling (${\tilde{g_{\phi \gamma}}} = 1$ - see text for description of the curves), and for $k_T = 0.5k_c$.