Small-scale fluctuations in the microwave background radiation and multiple gravitational lensing

We show here that multiple gravitational lensing of the microwave background radiation (MBR) by static compact objects significantly attenuates small-scale fluctuations in the MBR. Gravitational lensing, by altering trajectories of MBR photons reaching an observer, leads to (phase) mixing of photons from regions with different initial fluctuations. As a result of this diffusion process the original fluctuations are damped on scales up to several minutes of arc. We derive an equation that describes this process, and we give its general solution. We conclude that the present upper limits on the amplitude of the microwave background fluctuations on small scales cannot constrain theories of galaxy formation.