Galaxy-CMB Cross-Correlation as a Probe of Alternative Models of Gravity

Bekenstein's alternative to general relativity, TeVeS, reduces to Modified Newtonian Dynamics (MOND) in the galactic limit. On cosmological scales, the (potential well <-> overdensity) relationship is quite different than in standard general relativity. Here we investigate the possibility of cross-correlating galaxies with the cosmic microwave background (CMB) to probe this relationship. At redshifts of order 2, the sign of the CMB-galaxy correlation differs in TeVeS from that in general relativity. We show that this effect is detectable and hence can serve as a powerful discriminator of these two models of gravity.