Cosmological perturbation theory using the FFTLog: Formalism and connection to QFT loop integrals

Marko Simonović, Tobias Baldauf, Matias Zaldarriaga, John Joseph Carrasco, Juna A. Kollmeier

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52 Scopus citations


We present a new method for calculating loops in cosmological perturbation theory. This method is based on approximating a ΛCDM-like cosmology as a finite sum of complex power-law universes. The decomposition is naturally achieved using an FFTLog algorithm. For power-law cosmologies, all loop integrals are formally equivalent to loop integrals of massless quantum field theory. These integrals have analytic solutions in terms of generalized hypergeometric functions. We provide explicit formulae for the one-loop and the two-loop power spectrum and the one-loop bispectrum. A chief advantage of our approach is that the difficult part of the calculation is cosmology independent, need be done only once, and can be recycled for any relevant predictions. Evaluation of standard loop diagrams then boils down to a simple matrix multiplication. We demonstrate the promise of this method for applications to higher multiplicity/loop correlation functions.

Original languageEnglish (US)
Article number030
JournalJournal of Cosmology and Astroparticle Physics
Issue number4
StatePublished - Apr 9 2018


  • baryon acoustic oscillations
  • power spectrum

ASJC Scopus subject areas

  • Astronomy and Astrophysics


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