Cosmological parameters from velocities, cosmic microwave background and supernovae

We compare and combine likelihood functions of the cosmological parameters Omega (m), h and sigma (8), from peculiar velocities, cosmic microwave background (CMB) and type la supernovae. These three data sets directly probe the mass in the Universe, without the need to relate the galaxy distribution to the underlying mass via a 'biasing' relation. We include the recent results from the CMB experiments BOOMERANG and MAXIMA-1. Our analysis assumes a flat Lambda cold dark matter (Lambda CDM) cosmology with a scale-invariant adiabatic initial power spectrum and baryonic fraction as inferred from big-bang nucleosynthesis. We find that all three data sets agree well, overlapping significantly at the 2 sigma level. This therefore justifies a joint analysis, in which we find a joint best-fitting point and 95 per cent confidence limits of Omega (m) = 0.28 (0.17,0.39), h = 0.74 (0.64,0.86) and sigma (8) = 1.17 (0.98,1.37). In terms of the natural parameter combinations for these data sigma (8)Omega (0.6)(m) = 0.54 (0.40,0.73), Omega (m)h = 0.21 (0.16,0.27). Also for the best-fitting point, Q(rms-ps) = 19.7 muK and the age of the Universe is 13.2 Gyr.