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Title: How many e -folds should we expect from high-scale inflation?

Abstract

In this study, we address the issue of how many e -folds we would naturally expect if inflation occurred at an energy scale of order 10 16 GeV . We use the canonical measure on trajectories in classical phase space, specialized to the case of flat universes with a single scalar field. While there is no exact analytic expression for the measure, we are able to derive conditions that determine its behavior. For a quadratic potential V ( Φ ) = m 2 Φ 2 / 2 with m = 2 × 10 13 GeV and cutoff at M Pl = 2.4 × 10 18 GeV , we find an expectation value of 2 × 10 10 e -folds on the set of Friedmann-Robertson-Walker trajectories. For cosine inflation V ( Φ ) = Λ 4 [ 1 - cos ( Φ / f ) ] with f = 1.5 × 10 19 GeV , we find that the expected total number of e -folds is 50, which would just satisfy the observed requirements of our own Universe; if f is larger, more than 50 e -folds are generically attained. Finally, we conclude that one should expect a large amount of inflation in large-field models and more limited inflation in small-field (hilltop) scenarios.

Authors:
 [1];  [1]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Betty Moore Foundation
OSTI Identifier:
1596472
Alternate Identifier(s):
OSTI ID: 1180062
Grant/Contract Number:  
SC0011632; DGE-1144469; 776
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review. D, Particles, Fields, Gravitation and Cosmology
Additional Journal Information:
Journal Volume: 90; Journal Issue: 6; Journal ID: ISSN 1550-7998
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Remmen, Grant N., and Carroll, Sean M. How many e-folds should we expect from high-scale inflation?. United States: N. p., 2014. Web. doi:10.1103/PhysRevD.90.063517.
Remmen, Grant N., & Carroll, Sean M. How many e-folds should we expect from high-scale inflation?. United States. doi:10.1103/PhysRevD.90.063517.
Remmen, Grant N., and Carroll, Sean M. Mon . "How many e-folds should we expect from high-scale inflation?". United States. doi:10.1103/PhysRevD.90.063517. https://www.osti.gov/servlets/purl/1596472.
@article{osti_1596472,
title = {How many e-folds should we expect from high-scale inflation?},
author = {Remmen, Grant N. and Carroll, Sean M.},
abstractNote = {In this study, we address the issue of how many e-folds we would naturally expect if inflation occurred at an energy scale of order 1016 GeV. We use the canonical measure on trajectories in classical phase space, specialized to the case of flat universes with a single scalar field. While there is no exact analytic expression for the measure, we are able to derive conditions that determine its behavior. For a quadratic potential V(Φ)=m2Φ2/2 with m=2×1013 GeV and cutoff at MPl=2.4×1018 GeV, we find an expectation value of 2×1010 e-folds on the set of Friedmann-Robertson-Walker trajectories. For cosine inflation V(Φ)=Λ4[1-cos(Φ/f)] with f=1.5×1019 GeV, we find that the expected total number of e-folds is 50, which would just satisfy the observed requirements of our own Universe; if f is larger, more than 50 e-folds are generically attained. Finally, we conclude that one should expect a large amount of inflation in large-field models and more limited inflation in small-field (hilltop) scenarios.},
doi = {10.1103/PhysRevD.90.063517},
journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
issn = {1550-7998},
number = 6,
volume = 90,
place = {United States},
year = {2014},
month = {9}
}

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Cited by: 12 works
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Works referenced in this record:

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    Works referencing / citing this record:

    Global dynamics and inflationary center manifold and slow-roll approximants
    journal, January 2015

    • Alho, Artur; Uggla, Claes
    • Journal of Mathematical Physics, Vol. 56, Issue 1
    • DOI: 10.1063/1.4906081