Inflation in random Gaussian landscapes
Abstract
We develop analytic and numerical techniques for studying the statistics of slowroll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze smallfield inflation in a onedimensional landscape. We calculate the probability distributions for the maximal number of efolds and for the spectral index of density fluctuations n {sub s} and its running α {sub s} . These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of largefield inflation. These methods do not suffer from potential inconsistencies inherent in the Brownian motion technique, which has been used in most of the earlier treatments.
 Authors:
 Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)
 Publication Date:
 OSTI Identifier:
 22676188
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 05; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; BROWNIAN MOVEMENT; COMPUTERIZED SIMULATION; CORRELATION FUNCTIONS; CORRELATIONS; DENSITY; DISTRIBUTION; FLUCTUATIONS; INFLATIONARY UNIVERSE; ONEDIMENSIONAL CALCULATIONS; PROBABILITY; RANDOMNESS
Citation Formats
Masoumi, Ali, Vilenkin, Alexander, and Yamada, Masaki, Email: ali@cosmos.phy.tufts.edu, Email: vilenkin@cosmos.phy.tufts.edu, Email: Masaki.Yamada@tufts.edu. Inflation in random Gaussian landscapes. United States: N. p., 2017.
Web. doi:10.1088/14757516/2017/05/053.
Masoumi, Ali, Vilenkin, Alexander, & Yamada, Masaki, Email: ali@cosmos.phy.tufts.edu, Email: vilenkin@cosmos.phy.tufts.edu, Email: Masaki.Yamada@tufts.edu. Inflation in random Gaussian landscapes. United States. doi:10.1088/14757516/2017/05/053.
Masoumi, Ali, Vilenkin, Alexander, and Yamada, Masaki, Email: ali@cosmos.phy.tufts.edu, Email: vilenkin@cosmos.phy.tufts.edu, Email: Masaki.Yamada@tufts.edu. Mon .
"Inflation in random Gaussian landscapes". United States.
doi:10.1088/14757516/2017/05/053.
@article{osti_22676188,
title = {Inflation in random Gaussian landscapes},
author = {Masoumi, Ali and Vilenkin, Alexander and Yamada, Masaki, Email: ali@cosmos.phy.tufts.edu, Email: vilenkin@cosmos.phy.tufts.edu, Email: Masaki.Yamada@tufts.edu},
abstractNote = {We develop analytic and numerical techniques for studying the statistics of slowroll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze smallfield inflation in a onedimensional landscape. We calculate the probability distributions for the maximal number of efolds and for the spectral index of density fluctuations n {sub s} and its running α {sub s} . These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of largefield inflation. These methods do not suffer from potential inconsistencies inherent in the Brownian motion technique, which has been used in most of the earlier treatments.},
doi = {10.1088/14757516/2017/05/053},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 05,
volume = 2017,
place = {United States},
year = {Mon May 01 00:00:00 EDT 2017},
month = {Mon May 01 00:00:00 EDT 2017}
}

In the landscape perspective, our Universe begins with a quantum tunneling from an eternallyinflating parent vacuum, followed by a period of slowroll inflation. We investigate the tunneling process and calculate the probability distribution for the initial conditions and for the number of efolds of slowroll inflation, modeling the landscape by a smallfield onedimensional random Gaussian potential. We find that such a landscape is fully consistent with observations, but the probability for future detection of spatial curvature is rather low, P ∼ 10{sup −3}.


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