Friedmann-Lemaitre cosmologies via roulettes and other analytic methods

Shouxin Chen, Gary W. Gibbons, Yisong Yang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number056
JournalJournal of Cosmology and Astroparticle Physics
Issue number10
StatePublished - Oct 27 2015


  • cosmology of theories beyond the SM
  • dark energy theory
  • dark matter theory

ASJC Scopus subject areas

  • Astronomy and Astrophysics


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