Cosmological-parameter determination with microwave background maps

The angular power spectrum of the cosmic microwave background (CMB) contains information on virtually all cosmological parameters of interest, including the geometry of the Universe ($\ensuremath{\Omega}$), the baryon density, the Hubble constant ($h$), the cosmological constant ($\ensuremath{\Lambda}$), the number of light neutrinos, the ionization history, and the amplitudes and spectral indices of the primordial scalar and tensor perturbation spectra. We review the imprint of each parameter on the CMB. Assuming only that the primordial perturbations were adiabatic, we use a covariance-matrix approach to estimate the precision with which these parameters can be determined by a CMB temperature map as a function of the fraction of sky mapped, the level of pixel noise, and the angular resolution. For example, with no prior information about any of the cosmological parameters, a full-sky CMB map with 0.5\ifmmode^\circ\else\textdegree\fi{} angular resolution and a noise level of 15 \ensuremath{\mu}K per pixel can determine $\ensuremath{\Omega}$, $h$, and $\ensuremath{\Lambda}$ with standard errors of \ifmmode\pm\else\textpm\fi{}0.1 or better, and provide determinations of other parameters which are inaccessible with traditional observations. Smaller beam sizes or prior information on some of the other parameters from other observations improves the sensitivity. The dependence on the underlying cosmological model is discussed.