Cosmological parameters from cluster abundances, cosmic microwave background and IRAS

We combine information on cosmological parameters from cluster abundances, CMB primordial anisotropies and the IRAS 1.2 Jy galaxy redshift survey. We take as free parameters the present values of the total matter density of the universe, Ωm, the Hubble parameter, h, the linear theory rms fluctuations in the matter density within 8 h 1 Mpc spheres, σ8, and the IRAS biasing factor, bIRAS. We assume that the universe is spatially flat, with a cosmolo gical constant, and that structure formed from adiabatic initial fluc tuations with a Harrison-Zel’dovich power spectrum (i.e. the primordial spectral index n = 1). The nucleosynthesis value for the baryonic matter density Ωb = 0.019/h 2 is adopted. We use the full three- and four- dimensional likelihood functions for each data set and marginali se these to two- and one- dimensional distributions in a Bayesian way, integrating over th e other parameters. It is shown that the three data sets are in excellent agreement, with a best fit point of Ωm = 1 ΩΛ = 0.36, h = 0.54, σ8 = 0.74, and bIRAS = 1.08. This point is within one sigma of the minimum for each data set alone. Pairs of these data sets have their degen eracies in sufficiently different directions that using only two data sets at a time is suffic ient to place good constraints on the cosmological parameters. We show that the results from each of the three possible pairings of the data are also in good agreement. Finally, we combine all three data sets to obtain marginalised 68 per cent confidence intervals of 0 .30 < Ωm < 0.43, 0.48 < h < 0.59, 0.69 < σ8 < 0.79, and 1.01 < bIRAS < 1.16. For the best fit parameters the CMB quadrupole is Qrms ps = 18.0µK, the shape parameter of the mass power-spectrum is Γ = 0.15, the baryon density is Ωb = 0.066 and the age of the universe is 16.7 Gyr.