  We discuss the non-Gaussian contribution to the power spectrum covariance of
cosmic microwave background (CMB) anisotropies resulting through weak
gravitational lensing angular deflections and the correlation of deflections
with secondary sources of temperature fluctuations generated by the large scale
structure, such as the integrated Sachs-Wolfe effect and the Sunyave-Zel'dovich
effect. This additional contribution to the covariance of binned angular power
spectrum, beyond the well known cosmic variance and any associated instrumental
noise, results from a trispectrum, or a four point correlation function, in
temperature anisotropy data. With substantially wide bins in multipole space,
the resulting non-Gaussian contribution from lensing to the binned power
spectrum variance is insignificant out to multipoles of a few thousand and is
not likely to affect the cosmological parameter estimation through acoustic
peaks and the damping tail. The non-Gaussian contribution to covariance,
however, should be considered when interpreting binned CMB power spectrum
measurements at multipoles of a few thousand corresponding to angular scales of
few arcminutes and less.
