Description
Primary gravitational waves (PGWs) generated during inflation exhibit a
steep rise in the spectrum at small scales. So the spectrum must be regularized to
remove this unphysical rise. For an instantaneous transition from inflation to
radiation domination epoch, adiabatic regularization is not sufficient to obtain a
finite generic two point function (2PF) in real space. We require a continuous
effective potential (a''/a), as well as adiabatic regularization, to get a decreasing
spectrum at small scales, hence a finite generic 2PF. In this talk, it will be
illustrated that introducing smoother effective potentials lead to stronger
suppressions in the spectrum at small scales. Using the Born approximation, we
will show how the behavior of the regularized spectrum of PGWs at small scales
change, when it is evolved through smoother and smoother transitions from
inflation to the epochs of radiation and matter domination.
