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, Ω_m, the Hubble parameter, h, the linear theory rms fluctuations in the matter density within 8h^-1Mpc spheres, σ₈, and the IRAS biasing factor, b_IRAS. We assume that the universe is spatially flat, with a cosmological constant, and that structure formed from adiabatic initial fluctuations with a Harrison-Zel'dovich power spectrum (i.e. the primordial spectral index n=1). The nucleosynthesis value for the baryonic matter density Ω_b=0.019/h² is adopted. We use the full three- and four-dimensional likelihood functions for each data set and marginalize these to two- and one-dimensional distributions in a Bayesian way, integrating over the other parameters. It is shown that the three data sets are in excellent agreement, with a best-fitting point of Ω_m=1-Ω_Λ=0.36, h=0.54, σ₈=0.74, and b_IRAS=1.08. This point is within one sigma of the minimum for each data set alone. Pairs of these data sets have their degeneracies in sufficiently different directions that using only two data sets at a time is sufficient 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 marginalized 68per cent confidence intervals of 0.30<Ω_m<0.43, 0.48<h<0.59, 0.69<σ₈<0.79, and 1.01<b_IRAS<1.16. For the best-fitting parameters the CMB quadrupole is Q_rms-ps=18.0μK, the shape parameter of the mass power spectrum is Γ=0.15, the baryon density is Ω_b=0.066 and the age of the universe is 16.7Gyr.