Classification of Inflationary Einstein--Scalar--Field--Models via Catastrophe Theory

Abstract

Various scenarios of the initial inflation of the universe are distinguished by the choice of a scalar field {\em potential} $U(\varphi )$ which simulates a {\it temporarily} non--vanishing {\em cosmological term}. Our new method, which involves a reparametrization in terms of the Hubble expansion parameter $H$, provides a classification of allowed inflationary potentials and of the stability of the critical points. It is broad enough to embody all known {\it exact} solutions involving one scalar field as special cases. Inflation corresponds to the evolution of critical points of some catastrophe manifold. The coalescence of its nondegenerate critical points with the creation of a degenerate critical point corresponds the reheating phase of the universe. This is illustrated by several examples.

12 pages, REVTeX, no figures

References in corpus (5)

• Reheating after Inflation
• COBE, Gravitational Waves, Inflation and Extended Inflation
• Gravitational Stability of Boson Stars
• Stability of Non-Abelian Black Holes
• A New Method of Generating Exact Inflationary Solutions

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• Shear-free rotating inflation
• Eigenvalues of the Stewart-Lyth equation for inflation with a blue spectrum
• An alternate Hamiltonian formulation of fourth-order theories and its application to cosmology
• Cosmic Expansion via Axion-Induced Quintessence