Rayleigh Scattering and Microwave Background Fluctuations

During the recombination epoch, cosmic background photons couple not only tofree electrons through Thompson scattering, but also to the neutral hydrogenthrough Rayleigh scattering. This latter is ~2% effect for photons near thepeak of the photon energy distribution at z=800 and a ~0.2% effect at z=1100.Including Rayleigh scattering in the calculation reduces Silk damping at fixedredshift, alters the position of the surface of last scattering and alters thepropagation of acoustic waves. We estimate the amplitude of these effects. Forthe Microwave Anisotropy Probe (MAP), Rayleigh scattering increases theanisotropy spectrum by 0.1% at the most. For the highest frequencies of thePlanck Surveyor, the effects of Rayleigh scattering are much more dramatic(decreasing the anisotropy spectrum by 3% at \nu~550GHz and l~1000). Therelative difference between the spectra of low and high frequencies is imposedby an oscillation with a function of multipole l and the oscillation amplitudeis up to 0.5% between 100 and 550GHz. Rayleigh scattering also slows thedecoupling between radiation and matter, but the effect is undetectably small.Comment: 15 pages, including 4 figures. The coefficient of Rayleigh scattering cross section and some numbers corrected, figures rescaled, main conclusions not changed. ApJ in pres