  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) 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 he Hubble constant, Type 1a supernovae distances and
observations of galaxy clustering and peculiar velocities.

Astrophysics