Exact analytic solution for non-linear density fluctuation in a ΛcDM universe

Jaiyul Yoo, Jinn Ouk Gong

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a ΛCDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.

Original languageEnglish
Article number017
JournalJournal of Cosmology and Astroparticle Physics
Issue number7
StatePublished - 2016

Bibliographical note

Funding Information:
J.Y. is supported by the Swiss National Science Foundation and a Consolidator Grant of the European Research Council (ERC-2015-CoG grant 680886).

Publisher Copyright:
© 2016 IOP Publishing Ltd and Sissa Medialab srl .


  • cosmological perturbation theory
  • galaxy clustering
  • power spectrum


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