  We consider the production of gravitons in an inflationary cosmology by
approximating each epoch of change in the equation of state as sudden, from
which a simple analytic graviton mode function has been derived. We use this
mode function to compute the graviton spectral energy density and the
tensor-induced cosmic microwave background anisotropy. The results are then
compared to the numerical calculations which incorporate a smooth
radiation-matter phase transition. We find that the sudden approximation is a
fairly good method. Besides, in determining the frequency range and amplitude
of the mode function, we introduce a pre-inflationary radiation-dominated epoch
and use a physically sensible regularization method.
