From Local Velocities to Microwave Background

Details From Local Velocities to Microwave Background From Local Velocities to Microwave Background

1996-10-16

arxiv.org/abs/astro-ph/9610132v1

Astronomy and Astrophysics

Astrophysics

16 pages, 6 figures. Submitted to Ap.J

Scientific paper

10.1086/304884

The mass density field as extracted from peculiar velocities in our cosmological neighborhood is mapped back in time to the CMB in two ways. First, the density power spectrum ($P_k$) is translated into a temperature angular power spectrum of sub-degree resolution ($C_l$) and compared to observations. Second, the local density field is translated into a temperature map in a patch on the last-scattering surface of a distant observer. A likelihood analysis of the Mark III peculiar velocity data have constrained the range of parameters for $P_k$ within the family of COBE-normalized CDM models (Zaroubi et al 1996), favoring a slight tilt in the initial spectrum, $n<1$. The corresponding range of $C_l$'s is plotted against current observations, indicating that the CMB data can tighten the constraints further: only models with ``small'' tilt ($n\sim 0.9$) and ``high'' baryonic content ($\Omega_b \sim 0.1$) could survive the two data sets simultaneously. The local mass density field that has been recovered from the velocities via a Wiener method is convolved with a Boltzmann calculation to recover $10'$ resolution temperature maps as viewed from different directions. The extent of the CMB patch and the amplitude of fluctuations depend on the choice of cosmological parameters, e.g., the local $100\hmpc$ sphere corresponds to $90'$ to $30'$ at the CMB for $\Omega$ between 1 and 0 respectively. The phases of the temperature map are correlated with those of the density field, contrary to the contribution of the 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.

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