Adiabatic regularization of power spectrum and stress tensor of relic gravitational wave without low-frequency distortion

Understand

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.