Diffusing nonlocal inflation: Solving the field equations as an initial value problem
Abstract
There has been considerable recent interest in solving nonlocal equations of motion which contain an infinite number of derivatives. Here, focusing on inflation, we review how the problem can be reformulated as the question of finding solutions to a diffusionlike partial differential equation with nonlinear boundary conditions. Moreover, we show that this diffusionlike equation, and hence the nonlocal equations, can be solved as an initial value problem once nontrivial initial data consistent with the boundary conditions is found. This is done by considering linearized equations about any field value, for which we show that obtaining solutions using the diffusionlike equation is equivalent to solving a local but infinite field cosmology. These local fields are shown to consist of at most two canonically normalized or phantom fields together with an infinite number of quintoms. We then numerically solve the diffusionlike equation for the full nonlinear case for two string field theory motivated models.
 Authors:

 Department of Applied Mathematics and Theoretical Physics, Wilberforce Road, Cambridge, CB3 9AN (United Kingdom)
 Publication Date:
 OSTI Identifier:
 21250827
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review. D, Particles Fields
 Additional Journal Information:
 Journal Volume: 78; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.78.063519; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 05562821
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUNDARY CONDITIONS; COSMOLOGY; EQUATIONS OF MOTION; FIELD EQUATIONS; FIELD THEORIES; INFLATION; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS
Citation Formats
Mulryne, D J, and Nunes, N J. Diffusing nonlocal inflation: Solving the field equations as an initial value problem. United States: N. p., 2008.
Web. doi:10.1103/PHYSREVD.78.063519.
Mulryne, D J, & Nunes, N J. Diffusing nonlocal inflation: Solving the field equations as an initial value problem. United States. https://doi.org/10.1103/PHYSREVD.78.063519
Mulryne, D J, and Nunes, N J. Mon .
"Diffusing nonlocal inflation: Solving the field equations as an initial value problem". United States. https://doi.org/10.1103/PHYSREVD.78.063519.
@article{osti_21250827,
title = {Diffusing nonlocal inflation: Solving the field equations as an initial value problem},
author = {Mulryne, D J and Nunes, N J},
abstractNote = {There has been considerable recent interest in solving nonlocal equations of motion which contain an infinite number of derivatives. Here, focusing on inflation, we review how the problem can be reformulated as the question of finding solutions to a diffusionlike partial differential equation with nonlinear boundary conditions. Moreover, we show that this diffusionlike equation, and hence the nonlocal equations, can be solved as an initial value problem once nontrivial initial data consistent with the boundary conditions is found. This is done by considering linearized equations about any field value, for which we show that obtaining solutions using the diffusionlike equation is equivalent to solving a local but infinite field cosmology. These local fields are shown to consist of at most two canonically normalized or phantom fields together with an infinite number of quintoms. We then numerically solve the diffusionlike equation for the full nonlinear case for two string field theory motivated models.},
doi = {10.1103/PHYSREVD.78.063519},
url = {https://www.osti.gov/biblio/21250827},
journal = {Physical Review. D, Particles Fields},
issn = {05562821},
number = 6,
volume = 78,
place = {United States},
year = {2008},
month = {9}
}