Axion as a fuzzy dark matter candidate: proofs in different gauges
Abstract
Axion as a coherently oscillating massive scalar field is known to behave as a zeropressure irrotational fluid with characteristic quantum stress on a small scale. In relativistic perturbation theory, the case was proved in the axioncomoving gauge up to fully nonlinear and exact order. Our basic assumption is that the field is oscillating with Compton frequency and the Compton wavelength is smaller than the horizon scale. Here, we revisit the relativistic proof to the linear order in the other gauge conditions. We show that the same equation for density perturbation known in the nonrelativistic treatment can be derived in two additional gauge conditions: the zeroshear gauge and the uniformcurvature gauge. The uniformexpansion gauge fails to get the aimed equation, and the quantum stress term is missing in the synchronous gauge. For comparison, we present the relativistic density perturbation equations in the zeropressure fluid in these gauge conditions. Except for the comoving and the synchronous gauge, the equations strikingly differ from the axion case. We clarify that the relativistic analysis based on time averaging is valid for scales larger than the Compton wavelength. Below the Compton wavelength, the field is not oscillating, and our oscillatory ansatz does not apply. We suggest an equation valid in all scales in the comoving gauge. For comparison, we review the nonrelativistic quantum hydrodynamics and present the Schrödinger equation to firstorder postNewtonian expansion in the cosmological context.
 Publication:

Journal of Cosmology and Astroparticle Physics
 Pub Date:
 March 2022
 DOI:
 10.1088/14757516/2022/03/001
 arXiv:
 arXiv:2109.05436
 Bibcode:
 2022JCAP...03..001H
 Keywords:

 cosmological perturbation theory;
 axions;
 dark matter theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 11 pages, no figure