Cosmic variance

Cosmic variance is the sampling uncertainty caused by observing only one realization of a cosmological random field. For a Gaussian isotropic full-sky temperature field and an ideal noiseless estimate, $\mathrm{Var}({\hat{C}}_{\ell })=2C_{\ell }^2/(2\ell +1)$ because there are only $2\ell +1$ independent real angular degrees of freedom.