Oscillating gravitational potential due to ultralight axion: Linear theory

Abstract

We derive oscillating gravitational potential caused by an ultralight axion as the cosmic dark matter, assuming the Compton wavelength smaller than the horizon scale. Both the quantum stress in density perturbation and the quantum oscillation of the gravitational potential are derived in the zero-shear gauge. By comparing the density, velocity and potential perturbation equations, we show that the axion fluid in relativistic analysis is quite different from the relativistic and Newtonian zero-pressure fluids, corresponding to Newtonian fluid only in the density perturbation. Relativistic perturbation analyses are made in the zero-shear gauge. (C) 2022 Elsevier B.V. All rights reserved.