Small-scale microwave background anisotropies implied by large-scale data

Abstract

In the absence of reheating microwave background radiation (MBR) anisotropies on arcminute scales depend uniquely on the amplitude and the coherence length of the primordial density fluctuations (PDFs). These can be determined from the recent data on galaxy correlations, xi(r), on linear scales (APM survey). We develop here expressions for the MBR angular correlation function, C(theta), on arcminute scales in terms of the power spectrum of PDFs and demonstrate their accuracy by comparing with detailed calculations of MBR anisotropies. We then show how to evaluate C(theta) directly in terms of the observed xi(r) and show that the APM data give information on the amplitude, C(O), and the coherence angle of MBR anisotropies on small scales.