TY - JOUR

T1 - Cosmological perturbation theory using the FFTLog

T2 - Formalism and connection to QFT loop integrals

AU - Simonović, Marko

AU - Baldauf, Tobias

AU - Zaldarriaga, Matias

AU - Carrasco, John Joseph

AU - Kollmeier, Juna A.

N1 - Funding Information:
M.S. gratefully acknowledges support from the Institute for Advanced Study and the Raymond and Beverly Sackler Foundation. M.Z. is supported by NSF grants AST-1409709 and PHY-1521097 and by the Canadian Institute for Advanced Research (CIFAR) program on Gravity and the Extreme Universe.
Funding Information:
urdson, Zachary Slepian, Gabriele Trevisan and Zvonimir Vlah for many useful discussions. J. J. M. C. is supported by the European Research Council under ERC-STG-639729, preQFT: Strategic Predictions for Quantum Field Theories. M.S. gratefully acknowledges support from the Institute for Advanced Study and the Raymond and Beverly Sackler Foundation. M.Z. is supported by NSF grants AST-1409709 and PHY-1521097 and by the Canadian Institute for Advanced Research (CIFAR) program on Gravity and the Extreme Universe.
Publisher Copyright:
© 2018 IOP Publishing Ltd and Sissa Medialab.

PY - 2018/4/9

Y1 - 2018/4/9

N2 - 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.

AB - 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.

KW - baryon acoustic oscillations

KW - power spectrum

UR - http://www.scopus.com/inward/record.url?scp=85047257502&partnerID=8YFLogxK

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U2 - 10.1088/1475-7516/2018/04/030

DO - 10.1088/1475-7516/2018/04/030

M3 - Article

AN - SCOPUS:85047257502

SN - 1475-7516

VL - 2018

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

IS - 4

M1 - 030

ER -