Perturbation approach to the Hill equation with a slowly varying parameter with application to the inflationary cosmology

DOI10.1063/1.5052341zbMath1408.83053arXiv1901.09914OpenAlexW2901091710WikidataQ128927041 ScholiaQ128927041MaRDI QIDQ4561717

V. A. Koutvitsky, Eugene M. Maslov

Publication date: 12 December 2018

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.09914

zbMATH Keywords

expanding universeinflationary cosmologyparametric resonanceperturbation approachHill equationfluctuations of the inflaton scalar field

Mathematics Subject Classification ID

Relativistic cosmology (83F05) Asymptotic expansions of solutions to PDEs (35C20) Methods of quantum field theory in general relativity and gravitational theory (83C47) Resonance in context of PDEs (35B34) Approximation procedures, weak fields in general relativity and gravitational theory (83C25)

Cites Work

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• The singular Hill equation and generalized Lindemann-Stieltjes method
• Response of a single-degree-of-freedom system to a non-stationary principal parametric excitation
• On the oscillation-driven cosmological expansion at the post-inflationary stage
• Parametric instability of the real scalar pulsons
• Non-stationary parametric oscillations
• Instability of coherent states of a real scalar field
• Inflation without Slow Roll
• Nonperturbative dynamics of reheating after inflation: A review
• Dynamics of first-order phase transitions in the \(\phi^4- \phi^6\) model caused by the parametric instability of the metastable vacuum

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