Chervon S., Fomin I., Yurov V., Yurov A. Scalar Field Cosmology

World Scientific, 2019. — 287 p. — (Series on the Foundations of Natural Science and Technology 13). — ISBN: 9811205078.This monograph discusses cosmological inflation and provides exact and slow roll solutions. It also reviews new and advanced approaches of exact solutions construction with canonical scalar fields, including application of generating functions methods, the superpotential and many others. This book presents the reduction of the Friedmann equation to the Abel equation, which is a very useful tool in cosmology. It offers new solutions and discusses its properties.
Additionally, it touches upon the role of phantom scalar field cosmology and analyzes phantonical models. It describes brane cosmology with scalar fields, providing exact solutions construction using the superpotential method as well as Darboux transformations.
This book provides detailed calculations throughoutA canonical scalar field in cosmology
Inflationary models with a canonical scalar field
Methods of exact solutions’ construction
Advanced methods of exact solutions’ construction
Approximated methods
Advanced methods of exact solutions’ construction
Cosmological perturbations
Cosmological perturbations
Friedmann vs Abel equations: A connection
The Abel equation and how to derive the unknown superpotentials
The Abel equation and the inflationary dynamics
The phantom fields
Phantom energy and symmetric cosmological solutions
Phantom multiverse: a curious synergy of cosmology and particle physics
Branes
Nonsingular solutions on the brane and in the bulk
The singular brane solutions with a finite scale factor
The exact cosmologies on the brane