Cosmic confusion: degeneracies among cosmological parameters derived from measurements of microwave background anisotropies

In the near future, observations of the cosmic microwave background (CMB) anisotropies will provide accurate determinations of many fundamental cosmological parameters. In this paper, we analyse degeneracies among cosmological parameters to illustrate some of the limitations inherent in CMB parameter estimation. For simplicity, throughout our analysis we assume a cold dark matter universe with power-law adiabatic scalar and tensor fluctuation spectra. We show that most of the variance in cosmological parameter estimates is contributed by a small number (two or three) of principal components. An exact likelihood analysis shows that the usual Fisher matrix approach can significantly overestimate the errors on cosmological parameters. We show that small correlated errors in estimates of the CMB power spectrum at levels well below the cosmic variance limits (caused, for example, by Galactic foregrounds or scanning errors) can lead to significant biases in cosmological parameters. Estimates of cosmological parameters can be improved very significantly by applying theoretical restrictions to the tensor component, and external constraints derived from more conventional astronomical observations such as measurements of the Hubble constant, Type la supernovae distances and observations of galaxy clustering and peculiar velocities.