Kinetically dominated curved universes: Logolinear series expansions. (arXiv:1901.07540v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Handley_W/0/1/0/all/0/1">Will Handley</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Lasenby_A/0/1/0/all/0/1">Anthony Lasenby</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Hobson_M/0/1/0/all/0/1">Mike Hobson</a>
We develop a method for computing series expansions out of a singularity 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 expanding out of a singularity in a pre-inflationary
phase of the universe. We develop mathematical techniques for generating these
expansions, and apply them to polynomial and Starobinsky inflationary
potentials. This paper is the first in a programme of work on kinetically
dominated curved universes, for which such power series are essential. Code for
analytic and numerical computation of logolinear series is provided on GitHub.
We develop a method for computing series expansions out of a singularity 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 expanding out of a singularity in a pre-inflationary
phase of the universe. We develop mathematical techniques for generating these
expansions, and apply them to polynomial and Starobinsky inflationary
potentials. This paper is the first in a programme of work on kinetically
dominated curved universes, for which such power series are essential. Code for
analytic and numerical computation of logolinear series is provided on GitHub.
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