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Title: Curvature perturbations in the effective field theory of inflation

Abstract

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

Authors:
ORCiD logo [1]; ORCiD logo [1];  [1]
  1. Univ. of Chicago, IL (United States)
Publication Date:
Research Org.:
Univ. of Chicago, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1593847
Grant/Contract Number:  
SC0009924; FG02-13ER41958
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 100; Journal Issue: 12; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
Inflation; Particles & Fields; Gravitation; Cosmology & Astrophysics

Citation Formats

Lagos, Macarena, Lin, Meng-Xiang, and Hu, Wayne. Curvature perturbations in the effective field theory of inflation. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.123507.
Lagos, Macarena, Lin, Meng-Xiang, & Hu, Wayne. Curvature perturbations in the effective field theory of inflation. United States. doi:10.1103/PhysRevD.100.123507.
Lagos, Macarena, Lin, Meng-Xiang, and Hu, Wayne. Wed . "Curvature perturbations in the effective field theory of inflation". United States. doi:10.1103/PhysRevD.100.123507.
@article{osti_1593847,
title = {Curvature perturbations in the effective field theory of inflation},
author = {Lagos, Macarena and Lin, Meng-Xiang and Hu, Wayne},
abstractNote = {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},
doi = {10.1103/PhysRevD.100.123507},
journal = {Physical Review D},
number = 12,
volume = 100,
place = {United States},
year = {2019},
month = {12}
}

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