Relativistic Axion with Nonrelativistic Momenta: A Robust Bound on Minimal ALP Dark Matter

TL;DR

This paper establishes a robust lower bound on the decay constant of axion-like particles (ALPs) as dark matter, demonstrating that nonrelativistic modes do not evade the limit and exploring the transition to relativistic behavior and domain wall formation.

Contribution

It proves that the existing bound on ALP decay constant holds even when nonzero-momentum modes dominate, extending previous results beyond homogeneous zero-momentum assumptions.

Findings

The bound remains valid with nonrelativistic modes dominating.

ALPs behave as relativistic radiation if the limit is violated.

Domain walls form when the typical momentum is small.

Abstract

The axion-like particle (ALP), a pseudo Nambu-Goldstone boson that couples to two photons, has been studied extensively in recent years as a dark matter candidate. For initial field configurations in a minimal ALP model explaining the observed dark matter abundance, we need the potential height to exceed the ALP energy density at redshift $z\approx 5.5\times 10^{6}$ leading to: $$ f_{\phi}\gtrsim4\times10^{13}\,{GeV}\,\biggl(\frac{10^{-18}\,eV}{m_{\phi}}\biggr), $$ where $m_{\phi}$ and $f_{\phi}$ denote the ALP mass and decay constant, respectively. This bound is known for the ALP dark matter dominated by the homogeneous zero-momentum mode, under the requirement that coherent oscillations begin early enough to satisfy the late-forming dark matter constraint. One loop hole to evade this limit may be to introduce a large amount of the non-relativistic modes of the ALP with non-vanishing momenta. Here we show that the same limit remains valid even if nonzero-momentum modes dominate. Interestingly, when $nonrelativistic$ gradient modes prevail, the ALP behaves $relativistic$ radiation rather than matter, if it violates the limit. Moreover, if the typical momentum is sufficiently small, Baumkuchen-like domain walls form, which play an important role in understanding the transition.