We present a method for calculating large numbers of power spectra $C_l$ and $P\left(k\right)\mathrm{}$ that accelerates CMBFAST by a factor around ${10}^3$ without appreciable loss of accuracy, then apply it to constrain 11 cosmological parameters from current cosmic microwave background (CMB) and large scale structure (LSS) data. While the CMB alone still suffers from several degeneracies, allowing, e.g., closed models with strong tilt and tensor contributions, the shape of the real space power spectrum of galaxies from the IRAS Point Source Catalogue Redshift (PSCz) survey breaks these degeneracies and helps place strong constraints on most parameters. At 95% confidence, the combined CMB and LSS data imply a baryon density $0.020<\mathrm{}{\omega }_{\mathrm{b}}<0.037,$ dark matter density $0.10<\mathrm{}{\omega }_{\mathrm{dm}}<0.32\mathrm{}$ with a neutrino fraction $f_{\nu }<38\%,$ vacuum density ${\Omega }_{\Lambda }<0.76,$ curvature $-0.19<\mathrm{}{\Omega }_{\mathrm{k}}<0.10,$ scalar tilt $0.86<\mathrm{}{n}_s<1.16,$ and reionization optical depth $\tau <\mathrm{0.44.}\mathrm{}$ These joint constraints are quite robust, changing little when we impose priors on the Hubble parameter, tilt, flatness, gravity waves or reionization. Adding nucleosynthesis and neutrino priors on the other hand tightens constraints considerably, requiring ${\Omega }_{\Lambda }>0.49\mathrm{}$ and a red-tilt, $n_s<1.\mathrm{}$ The analysis allows a number of consistency tests to be made, all of which pass. At the 95% level, the flat scalar “concordance model” with ${\Omega }_{\Lambda }=0.62,\hspace{0.5em}{\omega }_{\mathrm{dm}}=0.13,\hspace{0.5em}{\omega }_{\mathrm{b}}=0.02,\hspace{0.5em}{f}_{\nu }\sim 0,\hspace{0.5em}{n}_s=0.9,\hspace{0.5em}\tau =0.1,\hspace{0.5em}h=0.63\mathrm{}$ is consistent with the CMB and LSS data considered here, with big bang nucleosynthesis, cluster baryon fractions and cluster abundance. The inferred PSCz bias $b\sim 1.2$ agrees with the value estimated independently from redshift space distortions. The inferred cosmological constant value agrees with the one derived independently from SNIa studies. Cosmology seems to be on the right track.

• Received 15 August 2000

DOI:https://doi.org/10.1103/PhysRevD.63.043007