Background-Enhanced Axion Force by Axion Dark Matter

Abstract: We investigate the influence of axion dark matter as a background on the spin-independent axion forces between nucleons. Notably, we find that the potential for axion forces scales from $1/r^3$ in a vacuum-only context to $1/r$ when the background effect is considered. Also, the magnitude of the axion force is substantially amplified in proportion to the number density of axion DM particles. These enhancements significantly improve the constraints on the axion decay constant by several orders of magnitude, across a broad range of axion masses, based on the fifth-force experiments such as the Casimir-less and torsion balance tests. This suggests that such experiments are more effective than previously understood in detecting axions.