Constraints on axionic fuzzy dark matter from light bending and Shapiro time delay

Abstract

Ultralight axion like particles (ALPs) of mass m_a∈ (10 to the power of negative 21 eV–10 to the power of negative 21 eV) with axion decay constant fa∼ 10 to the power of 17 GeV can be candidates for fuzzy dark matter (FDM). If celestial bodies like Earth and Sun are immersed in a low mass axionic FDM potential and if the ALPs have coupling with nucleons then the coherent oscillation of the axionic field results a long range axion hair outside of the celestial bodies. The range of the axion mediated Yukawa type fifth force is determined by the distance between the Earth and the Sun which fixes the upper bound of the mass of axion as ma≲10 to the power of negative 18 eV. The long range axionic Yukawa potential between the Earth and Sun changes the gravitational potential between them and contribute to the light bending and the Shapiro time delay. From the observational uncertainties of those experiments, we obtain an upper bound on the axion decay constant as fa≲ 9.85× 10 to the power of 6 GeV, which is the stronger bound obtained from Shapiro time delay. This implies if ALPs are FDM, then they do not couple to quarks.