Friedmann-Lemaitre Cosmologies via Roulettes and Other Analytic Methods
Abstract
In this work a series of methods are developed for understanding the Friedmann equation when it is beyond the reach of the Chebyshev theorem. First it will be demonstrated that every solution of the Friedmann equation admits a representation as a roulette such that information on the latter may be used to obtain that for the former. Next the Friedmann equation is integrated for a quadratic equation of state and for the Randall--Sundrum II universe, leading to a harvest of a rich collection of new interesting phenomena. Finally an analytic method is used to isolate the asymptotic behavior of the solutions of the Friedmann equation, when the equation of state is of an extended form which renders the integration impossible, and to establish a universal exponential growth law.
Keywords
Cite
@article{arxiv.1508.06750,
title = {Friedmann-Lemaitre Cosmologies via Roulettes and Other Analytic Methods},
author = {Shouxin Chen and Gary W. Gibbons and Yisong Yang},
journal= {arXiv preprint arXiv:1508.06750},
year = {2015}
}
Comments
40 pages, no figures