Test of the Gravitational Force Law on Cosmological Scales Using the Kinematic Sunyaev-Zeldovich Effect

The mean pairwise velocity of massive halos reflects the gravitational force law on cosmic scales. We combine cosmic microwave background intensity maps from the Atacama Cosmology Telescope and a galaxy catalog from the Sloan Digital Sky Survey to estimate the mean pairwise velocity using the kinematic Sunyaev-Zeldovich (kSZ) effect. On scales from 30 to 230 megaparsecs, we constrain the gravitational acceleration between pairs of halos at separation r to be g∝1/rⁿ with n=2.1±0.3, which is consistent with Newtonian gravity in an expanding spacetime (i.e., the standard ΛCDM model). This constraint shows agreement with an inverse quadratic radial dependence over the large distances separating galaxy halos, as expected in standard cosmology. Upcoming surveys have the potential to rule out n=1 at 10σ significance. Our results establish the kSZ effect as a powerful tool for testing gravity on cosmological scales.