The next cosmology seminar takes place on Friday 26th of June, room E349 at 2:00pm. We will have the pleasure to listen to Alipriyo Hoory from the Indian Institute of Technology (Chennai, India).
At 2:00pm, room E349, Alipriyo Hoory will be talking about
Power spectrum of primary gravitational waves at high frequencies
Primary gravitational waves (PGWs) are generated from the quantum vacuum during inflation. In slow roll inflation, the power spectrum (PS) of PGWs over large scales, which leave the Hubble radius during inflation, is nearly scale-invariant. However, over very small scales, which never leave the Hubble radius, the PS of PGWs rises quadratically. In this talk, I will first argue that the PS has to be regularized in order to truncate the unphysical, quadratic rise at high frequencies. Assuming instantaneous transitions from inflation to the epochs of radiation and matter domination, I will discuss the results of adiabatic subtraction to regularize the PS of PGWs. Thereafter, I will describe the effects of smoothing the transition from inflation to radiation domination (to be precise, we smooth the ‘effective potential’ governing the equation of motion of PGWs) and discuss the impact of the smoothing on the regularized PS of PGWs. Lastly, I will utilize the Born approximation to examine the behavior of the regularized PS of PGWs over small scales when they are evolved through smoother and smoother transitions from inflation to the epochs of radiation and matter domination. I will show that, at small scales or, equivalently, at high frequencies, the suppression in the regularized PS of PGWs occurs more and more sharply as the transition is smoothed further and further. With the help of specific examples, I will also illustrate that, in the case of completely smooth transitions described by an infinitely differentiable ‘effective potential’, the regularized PS of PGWs exhibits an exponential suppression on small scales. I will conclude with a brief summary.