Comparing sharp and smooth transitions of the second slowroll parameter in singlefield inflation
Abstract
In singlefield inflation, violation of the slowroll approximation can lead to growth of curvature perturbation outside the horizon. This violation is characterized by a period with a large negative value of the second slowroll parameter. At an early time, inflation must satisfy the slowroll approximation, so the largescale curvature perturbation can explain the cosmic microwave background fluctuations. At intermediate time, it is viable to have a theory that violates the slowroll approximation, which implies amplification of the curvature perturbation on small scales. Specifically, we consider ultraslowroll inflation as the intermediate period. At late time, inflation should go back to the slow roll period so that it can end. This means that there are two transitions of the second slowroll parameter. In this paper, we compare two different possibilities for the second transition: sharp and smooth transitions. Focusing on effects generated by the relevant cubic selfinteraction of the curvature perturbation, we find that the bispectrum and oneloop correction to the power spectrum due to the change of the second slowroll parameter vanish if and only if the MukhanovSasaki equation for perturbation satisfies a specific condition called Wands duality. We also find in the case of sharp transition that, even though this duality is satisfied in the ultraslowroll and slowroll phases, it is severely violated at the transition so that the resultant oneloop correction is extremely large inversely proportional to the duration of the transition.
 Publication:

arXiv eprints
 Pub Date:
 May 2024
 DOI:
 10.48550/arXiv.2405.12145
 arXiv:
 arXiv:2405.12145
 Bibcode:
 2024arXiv240512145K
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory