  Adiabatic regularization is a method to remove UV divergences in quantum
fields in curved spacetime. For relic gravitational wave generated during
inflation, regularization on all $k$-modes of the power spectrum to 2nd
adiabatic order, and of the energy density and pressure to 4th order,
respectively, causes low-frequency distortions. To avoid these, we regularize
only the short modes inside the horizon during inflation (corresponding to the
present frequencies $f \gtrsim 10^{9}$Hz), and keep the long modes intact.
Doing this does not violate the energy conservation since the $k$-modes of RGW
are independent of each other during inflation. The resulting spectra are UV
convergent and simultaneously free of low-frequency distortion, and these
properties remain in the present spectra after evolution, in contrast to
regularization at the present time which has some distortion or irregularities.
The spectra generally exhibit quick oscillations in frequency domain, even if
the initial spectra during inflation have no oscillations. This pattern is due
to the interference between the positive and negative frequency modes developed
during cosmic expansion, and may be probed by future RGW detections.
