Vacuum and Gravitons of Relic Gravitational Waves, and Regularization of
  Spectrum and Energy-Momentum Tensor
  The spectrum of relic gravitational wave (RGW) contains high-frequency
divergences, which should be removed. We present a systematic study of the
issue, based on the exact RGW solution that covers the five stages, from
inflation to the acceleration, each being a power law expansion. We show that
the present RGW consists of vacuum dominating at $f>10^{11}$Hz and graviton
dominating at $f<10^{11}$Hz, respectively. The gravitons are produced by the
four cosmic transitions, mostly by the inflation-reheating one. We perform
adiabatic regularization to remove vacuum divergences in three schemes: at
present, at the end of inflation, and at horizon-exit, to the 2-nd adiabatic
order for the spectrum, and the 4-th order for energy density and pressure. In
the first scheme a cutoff is needed to remove graviton divergences. We find
that all three schemes yield the spectra of a similar profile, and the
primordial spectrum defined far outside horizon during inflation is practically
unaffected. We also regularize the gauge-invariant perturbed inflaton and the
scalar curvature perturbation by the last two schemes, and find that the scalar
spectra, the tensor-to-scalar ratio, and the consistency relation remain
unchanged.
