Indirect Parametric Resonance of the Electromagnetic Field Driven by an Oscillating SU(2) Dark Matter Condensate

TL;DR

This paper analyzes how an oscillating SU(2) dark matter condensate can indirectly induce parametric resonance in electromagnetic fields via a pseudoscalar mediator, revealing conditions for resonance and enhancement.

Contribution

It provides an analytical study of indirect parametric resonance driven by an SU(2) condensate affecting electromagnetic helicity modes through a pseudoscalar coupling.

Findings

Homogeneous oscillating SU(2) background acts as a periodic source for pseudoscalar field.

Resonance conditions are derived using Hill and Mathieu equations.

Two-stage enhancement process identified: Q to χ to U(1).

Abstract

We study a local patch of an axion-like dark sector in Minkowski spacetime, containing an initially homogeneous and isotropic non-Abelian $SU(2)$ condensate, and a real pseudoscalar field $\chi$, coupled to an Abelian $U(1)$ gauge field which could be that of usual electromagnetism. The pseudoscalar couples directly to both gauge sectors through Chern-Simons interactions, while the $U(1)$ field couples to the $SU(2)$ condensate only indirectly, through the pseudoscalar. We show analytically that a homogeneous oscillating $SU(2)$ background $Q(t)$ acts as a periodic source for $\chi$, generating a homogeneous oscillatory condensate $\dot{\chi}$ that in turn modulates the frequency of the $U(1)$ helicity modes. In the linear regime this produces a Hill equation, and when the first harmonic dominates it reduces to a Mathieu equation. We derive the approximate resonance conditions, the leading Floquet exponent, and the conditions for a two-stage enhancement $Q \to \chi \to U(1)$. We also highlight an important point: in the exactly periodic, zero-bias limit, the indirect resonance is not intrinsically chiral, because the two Abelian helicities are related by a half-period time shift.