Cosmic Variance in CMB Anisotropies: From $1^{\circ}$ to COBE

Abstract

Cosmic Microwave Background (CMB) anisotropies that result from quantum fluctuations during inflation are explored and the impact of their ``cosmic variance'' on the ability to use existing data to probe inflationary models is studied. We calculate the rms temperature fluctuation, and its cosmic variance, for a number of experiments and for models with primordial power spectra which range from $n={1\over 2}$ to $1$. We find: (1) cosmic variance obscures the information which can be extracted, so a comparison of the rms temperature fluctuation on small scales with the COBE result can fix $n$ to only $\approx\pm 0.2$ at best; (2) measurements of the rms fluctuation on $1^{\circ}$ scales may not allow one to unambiguously infer the tensor contribution to the COBE anisotropy; (3) comparison of this contribution with the predictions of inflation are ambiguous if the quadrupole anisotropy alone is utilized. We discuss means for minimizing the uncertainty due to cosmic variance in comparisons between experiments.