2008/05/31 by David J. Mulryne, D. J. Mulryne, N. J. Nunes · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #advanced mathematical theories #astro-ph #hep-th
paper · pdf · doi:10.1103/physrevd.78.063519
published as Phys.Rev.D78:063519,2008 · 15 pages, 8 figures, references added, accepted for publication in Phys. Rev. D
arxiv created 2008/08/19 · openalex publication_date 2008/09/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.