Omega from the COBE-DMR anisotropy maps

Abstract

We have made a likelihood statistical analysis of the angular correlations in the {\it COBE}-DMR two-year sky maps by Monte Carlo simulation of the temperature fluctuations. We assume an open universe and consider as primordial power spectrum the Harrison-Zeldovich one, $P(k)=Ak$. We find that the flatness of the universe is not implied by the data. The quadrupole normalization amplitude, $Q_{rms-PS}$, is related to the density parameter, $\Omega$, by $Q_{rms-PS} = 10.67 + 55.81 \Omega - 128.59 \Omega^2 + 81.26 \Omega^3\ \mu$K. We have determined the p.d.f. of $\Omega$ due to cosmic plus sampling (i.e. $20^\circ$ galactic cut) variance which generically shows a bimodal shape. The uncertainty as given by the r.m.s. is $\approx 0.35$, therefore to better constrain $\Omega$ experiments sensitive to higher multipoles ($l>20$) should be considered.