Curvature perturbations in the effective field theory of inflation

Journal Article · 04 December 2019 · Physical Review D

DOI: https://doi.org/10.1103/PhysRevD.100.123507 · OSTI ID:1593847

Lagos, Macarena  ^[1]; Lin, Meng-Xiang  ^[1]; Hu, Wayne ^[1]

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1. Univ. of Chicago, IL (United States)

We discuss the difference between various gauge-invariant quantities typically used in single-field inflation, namely synchronous $$ζ_s$$, comoving $$ζ_c$$, and unitary $$ζ_u$$ curvatures. We show that conservation of $$ζ_c$$ outside thehorizon 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: ultra-slow-roll (USR) andbraiding-ultra-slow-roll (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 separate universe and the usage of the $δN$ 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 $δN$ formalism can still be applied to calculate the primordial power spectrum of some gauge-invariant quantities such as $$ζ_u$$, although it breaks down for others such as the uniform-density curvature. In BUSR, we show that both $$ζ_u$$ and $$ζ_s$$ are conserved outside the horizon, but take different values. Additionally, since $$ζ_u$$ 6= $$ζ_c$$ we find that the prediction for observable curvature fluctuations after inflation does not reflect $$ζ_c$$ at horizon crossing during inflation and moreover involves not just $$ζ_u$$ at that epoch but also the manner in which the braiding phase ends

• Research Organization: Univ. of Chicago, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0009924; FG02-13ER41958
• OSTI ID: 1593847
• Journal Information: Physical Review D, Vol. 100, Issue 12; ISSN 2470-0010
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English