A New Method of Generating Exact Inflationary Solutions

Abstract

The mechanism of the initial inflation of the universe is based on gravitationally coupled scalar fields $\varphi$. Various scenarios are distinguished by the choice of an {\it effective self--interaction potential} $U(\varphi )$ which simulates a {\it temporarily} non--vanishing {\em cosmological term}. Using the Hubble expansion parameter $H$ as a new ``time" coordinate, we can formally derive the {\it general} Robertson--Walker metric for a {\em spatially flat} cosmos. Our new method provides a classification of allowed inflationary potentials and is broad enough to embody all known {\it exact} solutions involving one scalar field as special cases. Moreover, we present new inflationary and deflationary exact solutions and can easily predict the influence of the form of $U(\varphi )$ on density perturbations.

32 pages, REVTeX, 9 postscript figures (or hardcopy) available upon request, Cologne-thp-1994-H8

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• Arbitrary scalar field and quintessence cosmological models
• Dynamical instability of fluid spheres in the presence of a cosmological constant
• Cosmology with exponential potentials
• Why Does Gravity Ignore the Vacuum Energy?
• Cornell Potential: A Neural Network Approach
• The method of generating functions in exact scalar field cosmology
• The generalized Chaplygin-Jacobi gas
• Decoupling of the general scalar field mode and the solution space for Bianchi type I and V cosmologies coupled to perfect fluid sources
• Reconstructing the inflaton potential for an almost flat COBE spectrum
• Shear-free rotating inflation
• Jacobi stability analysis of scalar field models with minimal coupling to gravity in a cosmological background
• Classification of Inflationary Einstein--Scalar--Field--Models via Catastrophe Theory
• Multi-fluid cosmology in Einstein gravity: analytical solutions
• Self-interacting scalar field cosmologies: unified exact solutions and symmetries
• Bianchi V inflation in the Brans-Dicke theory?
• Another exact inflationary solution
• A Jacobian elliptic single-field inflation
• Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology
• The Andante Regime of Scalar Field Dynamics
• Thermodynamics of Modified Chaplygin-Jacobi Gas and Modified Chaplygin-Abel Gas: Stability Analysis and Observational Constraints
• Exact inflationary solutions
• Eigenvalues of the Stewart-Lyth equation for inflation with a blue spectrum