HOW COSMIC MICROWAVE BACKGROUND CORRELATIONS AT LARGE ANGLES RELATE TO MASS AUTOCORRELATIONS IN-SPACE

The Sachs-Wolfe effect is known to produce large angular scale fluctua tions in the cosmic microwave background radiation (CMBR) due to gravi tational potential fluctuations. We show how the angular correlation f unction of the CMBR can be expressed explicitly in terms of the mass a utocorrelation function xi(r) in the universe. We derive analytic expr essions for the angular correlation function and its multipole moments in terms of integrals over xi(r) or its second moment, J3(r), which d oes not need to satisfy the sort of integral constraint that xi(r) mus t. We derive similar expressions for bulk flow velocity in terms of xi and J3. One interesting result that emerges directly from this analys is is that, for all angles theta, there is a substantial contribution to the correlation function from a wide range of distance r and that t he radial shape of this contribution does not vary greatly with angle.