Axion as a cold dark matter candidate: Proof to fully nonlinear order

TL;DR

This paper rigorously proves that axions can serve as cold dark matter by deriving fully nonlinear relativistic hydrodynamic equations, showing their behavior matches that of zero-pressure cold dark matter on super-Jeans scales.

Contribution

It provides the first fully nonlinear relativistic proof confirming axions as cold dark matter candidates within Einstein's gravity framework.

Findings

Axions exhibit characteristic pressure and anisotropic stress starting from second-order perturbations.

The effective pressure in relativistic hydrodynamics is governed by the perturbed lapse function.

The Jeans scale for axions is of solar-system size, supporting their role as cold dark matter.

Abstract

We present a proof of the axion as a cold dark matter candidate to the fully nonlinear order perturbations based on Einstein's gravity. We consider the axion as a coherently oscillating massive classical scalar field without interaction. We present the fully nonlinear and exact, except for {\it ignoring} the transverse-tracefree tensor-type perturbation, hydrodynamic equations for an axion fluid in Einstein's gravity. We show that the axion has the characteristic pressure and anisotropic stress, the latter starts to appear from the second-order perturbation. But these terms do not directly affect the hydrodynamic equations in our axion treatment. Instead, what behaves as the effective pressure term in relativistic hydrodynamic equations is the perturbed lapse function and the relativistic result coincides exactly with the one known in the previous non-relativistic studies. The effective pressure term leads to a Jeans scale which is of the solar-system scale for conventional axion mass. As the fully nonlinear and relativistic hydrodynamic equations for an axion fluid coincide exactly with the ones of a zero-pressure fluid in the super-Jeans scale, we have proved the cold dark matter nature of such an axion in that scale.