A calculation of cosmic variance in cosmic microwave background anisotropy

We present a theoretical calculation of the variance \Delta C_l of the CMB anisotropy power spectrum \langle C_l\rangle caused by gravitational waves based on quantum field theory in an inflationary cosmology. We find that since the temporal phases of the waves are fixed and the degree of freedom of the components in C_l is limited by the gravition spin, \Delta C_l = \langle C_l\rangle and {\it does not decrease with l}. In addition, anisotropies at different scales are {\it correlated} with a finite width. This new statistics is then applied to construct the temperature correlation function