Direct signature of an evolving gravitational potential from the cosmic microwave background

Abstract

We show that a time dependent gravitational potential can be directly detected from cosmic microwave background (CMB) anisotropies. The signature can be measured by cross-correlating the CMB with the projected density field reconstructed from weak lensing distortions of the CMB itself. The cross-correlation gives a signal whenever there is a time dependent gravitational potential. This method traces dark matter directly and has a well defined redshift distribution of mass producing the lensing, thereby avoiding the problems plaguing other proposed cross-correlations. We show that both the Microwave Anisotropy Probe (MAP) and Planck satellites will be able to probe this effect for observationally relevant curvature and cosmological constant models, which will provide additional constraints on the cosmological parameters.