Abstract
Axion couplings to photons could induce photon-axion conversion in the
presence of magnetic fields in the Universe. The conversion could impact
various cosmic distance measurements such as luminosity distances to type Ia
supernovae and angular distances to galaxy clusters in different ways. We
consider different combinations of the most updated distance measurements to
constrain the axion-photon coupling. Depending on the models of magnetic field
in the intracluster medium, we find the upper bounds on axion-photon couplings
to be around $5 (10^-13 - 10^-12)$ (nG/$B$) GeV$^-1$ for axion
mass below $5 10^-13$ eV, where $B$ is the strength of the magnetic
field in the intergalactic medium. The bounds are determined by the shape of
Hubble rate as a function of redshift reconstructable from various distance
measurements, and insensitive to today's Hubble rate, of which there is a
tension between early and late cosmological measurements. As an appendix, we
discuss model building challenges to use photon-axion conversion to make type
Ia supernovae brighter to alleviate the Hubble problem/crisis.
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