Effects of regularization and smooth transitions on primary gravitational waves

Abstract: Inflation is the most attractive scenario for the generation of primordial perturbations. Primary gravitational waves (PGWs) are generated from the quantum vacuum when their modes are deep inside the Hubble radius during inflation. In the standard slow-roll inflationary scenario, the power spectrum of PGWs on large scales—corresponding to modes that exit the Hubble radius during inflation—is nearly scale-invariant. However, the spectrum over very small scales, which never leave the Hubble radius, behaves as k^2. If such a spectrum of PGWs has evolved until today, the dimensionless spectral energy density (SED) of these GWs today would behave as k^4 on small scales. 

In the first part of my talk, I will describe the behavior of the spectral energy density (SED) of PGWs at very high frequencies in simple cosmological scenarios and emphasize the necessity of adiabatic regularization. Assuming an instantaneous transition from inflation to radiation domination, I will outline the application of adiabatic regularization and present the resulting SED across a wide range of frequencies. While this regularization removes the k^4 rise at high frequencies, the SED remains nearly scale-invariant on small scales. In the later part of the talk, I will discuss the impact of smoothing the transition from inflation to radiation domination on the regularized SED of PGWs. I will also introduce the Born approximation as a useful tool and demonstrate that smoother transitions lead to sharper suppression of power at high frequencies. I will conclude by discussing the possible implications of the observation of the suppression in the SED of PGWs at high frequencies.