2025/10/13 by Zhou, Shuren, Zhang, Pengjie
#Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences
paper · doi:10.48550/arxiv.2510.11022
A key measure of gravity is the relation between the Weyl potential Ψ+Φ and the matter overdensity δm, capsulized as an effective gravitational constant G\rm light for light motion. Its value, together with the possible spatial and temporal variation, is essential in probing physics beyond Einstein gravity. However, the lack of an unbiased proxy of δm prohibits direct measurement of G\rm light. We point out that the equivalence principle ensures the dispersion measure (DM) of localized fast radio bursts (FRBs) as a good proxy of δm. We further propose a FRB-based method FG to directly measure G\rm light, combining galaxy-DM of localized FRBs and galaxy-weak lensing cross-correlations. The measurement, with a conservative cut k≤ 0.1h/Mpc, can achieve a precision of \lesssim 10% √105/N\rm FRB over 10 equal-width redshift bins at z\lesssim 1. The major systematic error, arising from the clustering bias of electrons traced by the FRB DM, is subdominant (∼ 5%). It can be further mitigated to the \lesssim 1% level, based on the gastrophysics-agnostic behavior that the bias of total baryonic matter (ionized diffuse gas, stars, neutral hydrogen, etc) approaches unity at sufficiently large scales. Therefore, FRBs shed light on gravitational physics across spatial and temporal scales spanning over 20 orders of magnitude.