Logolinear series expansions with applications to primordial cosmology

Abstract

We develop a method for computing series expansions for solutions to ordinary differential equations when the asymptotic form contains both linear and logarithmic terms. Such situations are common in primordial cosmology when considering series expansions out of a singularity in the equations arising from a pre-inflationary phase of the universe. We develop mathematical techniques for generating these series expansions, and apply them to polynomial and Starobinsky inflationary potentials with kinetic initial conditions. Code for analytic and numerical computation of logolinear series is provided on GitHub.

arXiv comment12 pages, 4 figures

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Cited by in corpus (7)

• Analytical approximations for curved primordial power spectra
• Primordial power spectra from $k$-inflation with curvature
• Separatrices in the Hamilton-Jacobi Formalism of Inflaton Models
• Kinetic dominance and psi series in the Hamilton-Jacobi formulation of inflaton models
• Kinetic dominance and the wavefunction of the universe
• On the slow roll expansion of one-field cosmological models
• Adaptive asymptotic solutions of inflationary models in the Hamilton-Jacobi formalism: Application to T-models