Self-interacting scalar field cosmologies: unified exact solutions and symmetries

Abstract

We investigate a mechanism that generates the exact solutions of scalar field cosmologies in a unified way. The procedure investigated here permits to recover allmost all known solutions, and allows one to derive new solutions as well. In particular, we derive and discuss one novel solution defined in terms of the Lambert function. The solutions are organized in a classification which depends on the choice of a generating function which we have denoted by $x(\varphi )$ that reflects the underlying thermodynamics of the model. We also analyse and discuss the existence of form invariances and dualities between solutions. A general way of defining the latter in an appropriate fashion for scalar fields is put forward.

arXiv comment6 figures, 30 pages

References in corpus (25)

• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• Inflation Dynamics and Reheating
• Pre-Big-Bang in String Cosmology
• The Pre-Big Bang Scenario in String Cosmology
• Reconstructing the Inflaton Potential --- an Overview
• Formalising the Slow-Roll Approximation in Inflation
• A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation
• Superstring Cosmology
• Constructing Phantom Cosmologies from Standard Scalar Field Universes
• Inflationary Models with Logarithmic Potentials
• The Behaviour of Varying-Alpha Cosmologies
• Phantom k-essence cosmologies
• Intermediate inflation in light of the three-year WMAP observations
• Dual interacting cosmologies and late accelerated expansion
• Generalised Scalar Field Potentials and Inflation
• On the potentials yielding cosmological scaling solutions
• Form Invariance of Differential Equations in General Relativity
• Exact Superstring Motivated Cosmological Models
• Inflationary potentials yielding constant scalar perturbation spectral indices
• An Inflationary Model with an Exact Perturbation Spectrum
• A New Method of Generating Exact Inflationary Solutions
• Unified phantom cosmologies
• Self-interacting scalar field cosmologies: unified exact solutions and symmetries
• Another exact inflationary solution
• Form invariant transformations between n-- and m-- dimensional flat Friedmann--Robertson--Walker cosmologies

Cited by in corpus (9)

• Arbitrary scalar field and quintessence cosmological models
• The method of generating functions in exact scalar field cosmology
• Canonical and phantom scalar fields as an interaction of two perfect fluids
• Multi-fluid cosmology in Einstein gravity: analytical solutions
• Self-interacting scalar field cosmologies: unified exact solutions and symmetries
• Extended tachyon field using form invariance symmetry
• Exact Solutions and Constraints on the Dark Energy Model in FRW Universe
• Dynamical analysis of the redshift drift in FLRW universes
• Self-interacting scalar field in (2+1) dimensions Einstein gravity with torsion