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 t he universe, Omega(m), the Hubble parameter, h, the linear theory rms fluct uations in the matter density within 8 h(-1) Mpc spheres, sigma(8), and the IRAS biasing factor, b(IRAS). We assume that the universe is spatially fla t, with a cosmological constant, and that structure formed from adiabatic i nitial fluctuations with a Harrison-Zel'dovich power spectrum (i.e. the pri mordial spectral index n = 1). The nucleosynthesis value for the baryonic m atter density Omega(b) = 0.019/h(2) is adopted. We use the full three- and four-dimensional likelihood functions for each data set and marginalize the se 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 exc ellent agreement, with a best-fitting point of Omega(m) = 1-Omega(Lambda) = 0.36, h = 0.54, sigma(8) = 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 onl y two data sets at a time is sufficient to place good constraints on the co smological parameters. We show that the results from each of the three poss ible pairings of the data are also in good agreement. Finally, we combine a ll three data sets to obtain marginalized 68 per cent confidence intervals of 0.30 < Omega(m) < 0.43, 0.48 < h < 0.59, 0.69 < sigma(8) < 0.79, and 1.0 1 < b(IRAS) < 1.16. For the best-fitting parameters the CMB quadrupole is Q (rms-ps) = 18.0 mu K, the shape parameter of the mass power spectrum is Gam ma = 0.15, the baryon density is Omega(b) = 0.066 and the age of the univer se is 16.7 Gyr.