How many $e$folds should we expect from highscale 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 ${10}^{16}\text{}\text{}\mathrm{GeV}$. 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 $V\left(\Phi \right)={m}^{2}{\Phi}^{2}/2$ with $m=2\times {10}^{13}\text{}\text{}\mathrm{GeV}$ and cutoff at ${M}_{\text{Pl}}=2.4\times {10}^{18}\text{}\text{}\mathrm{GeV}$, we find an expectation value of $2\times {10}^{10}$ $e$folds on the set of FriedmannRobertsonWalker trajectories. For cosine inflation $V\left(\Phi \right)={\mathrm{\Lambda}}^{4}[1\mathrm{cos}(\Phi /f\left)\right]$ with $f=1.5\times {10}^{19}\text{}\text{}\mathrm{GeV}$, 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 largefield models and more limited inflation in smallfield (hilltop) scenarios.
 Authors:

 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; DGE1144469; 776
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review. D, Particles, Fields, Gravitation and Cosmology
 Additional Journal Information:
 Journal Volume: 90; Journal Issue: 6; Journal ID: ISSN 15507998
 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 efolds should we expect from highscale inflation?. United States: N. p., 2014.
Web. doi:10.1103/PhysRevD.90.063517.
Remmen, Grant N., & Carroll, Sean M. How many efolds should we expect from highscale inflation?. United States. https://doi.org/10.1103/PhysRevD.90.063517
Remmen, Grant N., and Carroll, Sean M. Mon .
"How many efolds should we expect from highscale inflation?". United States. https://doi.org/10.1103/PhysRevD.90.063517. https://www.osti.gov/servlets/purl/1596472.
@article{osti_1596472,
title = {How many efolds should we expect from highscale inflation?},
author = {Remmen, Grant N. and Carroll, Sean M.},
abstractNote = {In this study, we address the issue of how many efolds 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 efolds on the set of FriedmannRobertsonWalker trajectories. For cosine inflation V(Φ)=Λ4[1cos(Φ/f)] with f=1.5×1019 GeV, we find that the expected total number of efolds is 50, which would just satisfy the observed requirements of our own Universe; if f is larger, more than 50 efolds are generically attained. Finally, we conclude that one should expect a large amount of inflation in largefield models and more limited inflation in smallfield (hilltop) scenarios.},
doi = {10.1103/PhysRevD.90.063517},
journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
number = 6,
volume = 90,
place = {United States},
year = {2014},
month = {9}
}
Web of Science
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