Joint estimation of cosmological parameters from CMB and IRAS data

Matthew Webster, S. L. Bridle, M. P. Hobson, A. N. Lasenby, Ofer Lahav, Graca Rocha

Published 1998-02-10, updated 1998-08-28Version 2

Observations of large scale structure (LSS) and the Cosmic Microwave Background (CMB) each place separate constraints on the values of cosmological parameters. We calculate a joint likelihood based on various CMB experiments and the IRAS 1.2Jy galaxy redshift survey and use this to find an overall optimum with respect to the free parameters. Our formulation self-consistently takes account of the underlying mass distribution, which affects both the CMB potential fluctuations and the IRAS redshift distortion. This not only allows more accurate parameter estimation, but also removes the parameter degeneracy which handicaps calculations based on either approach alone. The family of Cold Dark Matter (CDM) models analysed corresponds to a spatially-flat universe with an initially scale-invariant spectrum and a cosmological constant. Free parameters in the joint model are the mass density due to all matter (Omega_m), Hubble's parameter (h = H_0 / 100km/s Mpc^-1), the quadrupole normalisation of the CMB power spectrum (Q) in uK, and the IRAS light-to-mass bias (b_i). Throughout the analysis, the baryonic density (Omega_b) is required is to satisfy the nucleosynthesis constraint Omega_b h^2 = 0.024. Results from the two data sets show good agreement, and the joint optimum lies at Omega_m=0.39, h=0.53, Q=16.96uK, and b_i=1.21. The 68 per cent confidence intervals are: 0.29<Omega_m<0.53, 0.39<h<0.58, 15.34<Q<17.60, and 0.98<b_i<1.56. For the above parameters the normalisation and shape of the mass power-spectrum are sigma_8=0.67 and Gamma=0.15, and the age of the Universe is 16.5Gyr.