Curvature perturbations in the effective field theory of inflation
Abstract
We discuss the difference between various gaugeinvariant quantities typically used in singlefield inflation, namely synchronous ζ_{s}, comoving ζ_{c}, and unitary ζ_{u} curvatures. We show that conservation of ζ_{c} outside the horizon is quite restrictive on models as it leads to conservation of ζ_{s} and ζ_{u}, whereas the reverse does not hold. We illustrate the consequence of these differences with two inflationary models: ultraslowroll (USR) and braidingultraslowroll (BUSR). In USR, we show that out of the three curvatures, only ζ_{s} is conserved outside the horizon, and we connect this result to the concepts of a separate universe and the usage of the δ N formalism. We find that even though ζ_{s} is conserved, there is still a mild violation of the separate universe approximation in the continuity equation. Nevertheless, the δ N formalism can still be applied to calculate the primordial power spectrum of some gaugeinvariant quantities such as ζ_{u}, although it breaks down for others such as the uniformdensity curvature. In BUSR, we show that both ζ_{u} and ζ_{s} are conserved outside the horizon, but take different values. Additionally, since ζ_{u}≠ζ_{c}, we find that the prediction for observable curvature fluctuations after inflation does not reflect ζ_{c} at the horizon crossing during inflation and moreover involves not just ζ_{u} at that epoch but also the manner in which the braiding phase ends.
 Publication:

Physical Review D
 Pub Date:
 December 2019
 DOI:
 10.1103/PhysRevD.100.123507
 arXiv:
 arXiv:1908.08785
 Bibcode:
 2019PhRvD.100l3507L
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 Phys. Rev. D 100, 123507 (2019)