'Sample variance' in small-scale cosmic microwave background anisotropy experiments

Abstract

We discuss the effects of finite sky coverage and the uncertainty in extracting information about the power spectrum from experiments on small angular scales. In general the cosmic variance is enhanced by a factor of $4\pi/A$, where $A$ is the solid angle sampled by the experiment. As a rough guide, an experiment with sensitivity peaking at the $\ell$th multipole has to cover $\simgt\ell$ independent patches to have a lower ``sample variance'' than for a whole-sky measurement of the quadrupole. Our approach gives a relatively simple way of attaching an error bar to the theoretical prediction for a particular experiment, and thereby comparing theories with experimental results, without the need for computationally-intensive Maximum Likelihood or Monte Carlo calculations.