FROM LOCAL VELOCITIES TO MICROWAVE BACKGROUND

The mass-density field as extracted from peculiar velocities in our co smological neighborhood is mapped back in time to the cosmic microwave background (CMB) in two ways. First, the density power spectrum (P-k) is translated into a temperature angular power spectrum of subdegree resolution (C-l) and compared to observations. Second, the local densi ty field is translated into a temperature map in a patch on the last-s cattering surface of a distant observer. A likelihood analysis of the Mark III catalog of peculiar velocities have constrained the range of parameters for P-k within the family of COBE-normalized cold dark matt er (CDM) models, favoring a slight tilt in the initial spectrum, n < 1 . The corresponding range of C-l is plotted against current observatio ns, indicating that the CMB data can tighten the constraints further. only models with small tilt(n similar to 0.9) and high baryonic conten t (Omega(b) similar to 0.1) could survive the two data sets simultaneo usly. The local mass-density field that has been recovered from the ve locities via a Wiener method is convovled with a Boltzmann calculation to recover 10' resolution temperature maps as viewed from different d irections. The extent of the CMB patch and the amplitude of fluctuatio ns depend on the choice of cosmological parameters, e.g., the local 10 0 h(-1) Mpc sphere corresponds to 90'-30' at the CMB for Omega between 1 and 0, respectively. The phases of the temperature map are correlat ed with those of the density field, contrary to the contribution of th e Sachs-Wolfe effect alone. This correlation suggests the possibility of an inverse reconstruction of the underlying density field from CMB data with interesting theoretical implications.