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

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: $$f_{\varphi }\gtrsim 4\times 10^{13}GeV\left(\frac{10^{-18}eV}{m_{\varphi }}\right),$$ where $m_{\varphi }$ and $f_{\varphi }$ 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.

Comments: v2: 20 pages, 10figures; version to appear in JHEP; presentation improved, "Baumkuchen domain wall" is proposed