Publication: Separatrices in the Hamilton-Jacobi formalism of inflaton models.
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2020-04-01
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American Institute of Physics
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Abstract
We consider separatrix solutions of the differential equations for inflaton models with a single scalar field in a zero-curvature Friedmann-Lemaitre-Robertson-Walker universe. The existence and properties of separatrices are investigated in the framework of the Hamilton-Jacobi formalism, where the main quantity is the Hubble parameter considered as a function of the inflaton field. A wide class of inflaton models that have separatrix solutions (and include many of the most physically relevant potentials) is introduced, and the properties of the corresponding separatrices are investigated, in particular, asymptotic inflationary stages, leading approximations to the separatrices, and full asymptotic expansions thereof. We also prove an optimal growth criterion for potentials that do not have separatrices.
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© 2020 American Institute of Physics.
The financial support of the Spanish Ministerio de Economia y Competitividad under Project Nos. FIS2015-63966-P, PGC2018-094898B-I00, and PGC2018-098440-B-I00 is gratefully acknowledged. J.L.V. would like to thank the Departamento de Analisis Matematico y Matematica Aplicada of the Universidad Complutense de Madrid for his appointment as Honorary Professor.