Likelihood distribution for models with cosmological constant from COBE data

Abstract

Using COBE-DMR 4-year data, we find a general expression yielding the likelihood distribution in the 3-dimensional parameter space spanned by the spectral index $n$, the spectral amplitude $a_{10}$ and the false-vacuum density parameter $Ω_Λ$. Using such simple expression, the range of possible normalizations, within a given likelihood interval from top-likelihood normalization, is readily found, with fair approximation, for any model with total density parameter $Ω_o = 1$ and assigned $n$ and $Ω_Λ$.