http://arxiv.org/abs/2109.05436
Axion as a coherently oscillating massive scalar field is known to behave as a zero-pressure irrotational fluid with characteristic quantum stress on a small scale. In relativistic perturbation theory, the case was most conveniently proved in the axion-comoving gauge up to fully nonlinear and exact order. Our basic assumption is that the Compton wavelength is smaller than the horizon scale. Here, we revisit the relativistic proof to the linear order in the other gauge conditions. The comoving gauge, the zero-shear gauge, and the uniform-curvature gauge give {\it the same} equation for density perturbation known in the non-relativistic quantum mechanical treatment in {\it all} scales. On the other hand, the quantum stress term is missing in the synchronous gauge, and inconsistency is found in the uniform-expansion gauge. In the absence of quantum stress, the simple density perturbation equations of the axion in the zero-shear gauge and the uniform-curvature gauge were {\it not} expected. Even in the zero-pressure fluid, the equations in the two gauges coincide with the one in the comoving gauge {\it only} in the sub-horizon scale. We clarify that our analysis is valid for scales larger than the Compton wavelength, which is negligible compared with the cosmological scale. For comparison, we review the non-relativistic quantum hydrodynamics and present the Schr\”odinger equation to first-order post-Newtonian expansion in the cosmology context.
J. Hwang and H. Noh
Tue, 14 Sep 21
21/88
Comments: 10 pages, no figure
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