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 ${10}^{16}\mathrm{GeV}$. 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 $m=2\times {10}^{13}\mathrm{GeV}$ and cutoff at $M_{\text{Pl}}=2.4\times {10}^{18}\mathrm{GeV}$, we find an expectation value of $2\times {10}^{10}$ $e$-folds on the set of Friedmann-Robertson-Walker trajectories. For cosine inflation $V\left(\Phi \right)={\mathrm{\Lambda }}^4[1-\cos (\Phi /f\left)\right]$ with $f=1.5\times {10}^{19}\mathrm{GeV}$, 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 large-field models and more limited inflation in small-field (hilltop) scenarios.

Authors:

Remmen, Grant N. ^[1]; Carroll, Sean M. ^[1]

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+ Show Author Affiliations

1. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

Publication Date:

2014-09-22

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:

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