Exact Solutions for Nonlocal Nonlinear Field Equations in Cosmology

Abstract

A method for the search of exact solutions for equation of a nonlocal scalar field in a non-flat metric is considered. In the Friedmann-Robertson-Walker metric the proposed method can be used in the case of an arbitrary potential, with the exception of linear and quadratic potentials, and allows to get in quadratures solutions, which depend on two arbitrary parameters. Exact solutions have been found for an arbitrary cubic potential, which consideration is motivated by the string field theory, as well as for exponential, logarithmic and power potentials. It has been shown that one can add the k-essence field to the model to get exact solutions for all Einstein equations.

14 pages, v2: Section 5 added, accepted for publication in Theor. Math. Phys

References in corpus (43)

• A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
• k-Inflation
• Ghost Condensation and a Consistent Infrared Modification of Gravity
• Effective Field Theory for Inflation
• Starting the Universe: Stable Violation of the Null Energy Condition and Non-standard Cosmologies
• k-Essence, superluminal propagation, causality and emergent geometry
• p-Adic Mathematical Physics
• The Effective Theory of Quintessence: the w<-1 Side Unveiled
• Dynamics of $k$-essence
• A Review on Tachyon Condensation in Open String Field Theories
• Time Evolution in Superstring Field Theory on non-BPS brane.I. Rolling Tachyon and Energy-Momentum Conservation
• Localization of nonlocal theories
• Dynamics with Infinitely Many Derivatives: The Initial Value Problem
• Route to nonlocal cosmology
• p-adic Inflation
• Exactly Solvable SFT Inspired Phantom Model
• Bouncing and Accelerating Solutions in Nonlocal Stringy Models
• Nonlocal gravity and the diffusion equation
• Large Nongaussianity from Nonlocal Inflation
• Dynamics in Nonlocal Cosmological Models Derived from String Field Theory
• Time Lumps in Nonlocal Stringy Models and Cosmological Applications
• Cosmological tachyon from cubic string field theory
• Non-local SFT Tachyon and Cosmology
• Diffusing non-local inflation: Solving the field equations as an initial value problem
• Attractor scenarios and superluminal signals in k-essence cosmology
• On the Null Energy Condition and Cosmology
• Stretching the Inflaton Potential with Kinetic Energy
• Quantization of the Riemann Zeta-Function and Cosmology
• The New Ekpyrotic Ghost
• Tachyon solutions in boundary and cubic string field theory
• Nonlocal instantons and solitons in string models
• Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric
• Construction of Exact Solutions in Two-Fields Models and the Crossing of the Cosmological Constant Barrier
• Cosmological perturbations in SFT inspired non-local scalar field models
• Dynamics with Infinitely Many Time Derivatives in Friedmann-Robertson-Walker Background and Rolling Tachyon
• Kinks of open superstring field theory
• Noncommutative Field Theories and (Super)String Field Theories
• Localization of nonlocal cosmological models with quadratic potentials in the case of double roots
• Analysis of scalar perturbations in cosmological models with a non-local scalar field
• Cosmological rolling solutions of nonlocal theories
• Stringy Model of Cosmological Dark Energy
• Rolling Solution for Tachyon Condensation in Open String Field Theory
• Multi-scalar field cosmology from SFT: an exactly solvable approximation

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• Cosmological Models Based on a Statistical System of Scalar Charged Degenerate Fermions and an Asymmetric Higgs Scalar Doublet
• The self-consistent field method and the macroscopic universe consisting of a fluid and a black holes
• The Solution to the Differential Equation with Linear Damping describing a Physical Systems governed by a Cubic Energy Potential