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Numerical evaluation of the bispectrum in multiple field inflation

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journal contribution
posted on 2023-06-09, 04:30 authored by Mafalda Dias, Jonathan Frazer, David J Mulryne, David SeeryDavid Seery
We present a complete framework for numerical calculation of the power spectrum and bispectrum in canonical inflation with an arbitrary number of light or heavy fields. Our method includes all relevant effects at tree-level in the loop expansion, including (i) interference between growing and decaying modes near horizon exit; (ii) correlation and coupling between species near horizon exit and on superhorizon scales; (iii) contributions from mass terms; and (iv) all contributions from coupling to gravity. We track the evolution of each correlation function from the vacuum state through horizon exit and the superhorizon regime, with no need to match quantum and classical parts of the calculation; when integrated, our approach corresponds exactly with the tree-level Schwinger or 'in-in' formulation of quantum field theory. In this paper we give the equations necessary to evolve all two- and three-point correlation functions together with suitable initial conditions. The final formalism is suitable to compute the amplitude, shape, and scale dependence of the bispectrum in models with |fNL| of order unity or less, which are a target for future galaxy surveys such as Euclid, DESI and LSST. As an illustration we apply our framework to a number of examples, obtaining quantitatively accurate predictions for their bispectra for the first time. Two accompanying reports describe publicly-available software packages that implement the method.

Funding

Astronomy rolling grant; G0278; STFC-SCIENCE AND TECHNOLOGY FACILITIES COUNCIL; ST/I000976/1

Precisions tests of the inflationary scenario; G0918; EUROPEAN UNION; 308082

Philip Leverhulme Prize - David Seery; G0810; LEVERHULME TRUST; PLP-2011-157

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Journal of Cosmology and Astroparticle Physics

ISSN

1475-7516

Publisher

IOP Publishing

Issue

12

Volume

2016

Page range

033

Department affiliated with

  • Physics and Astronomy Publications

Research groups affiliated with

  • Astronomy Centre Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-01-03

First Open Access (FOA) Date

2017-12-20

First Compliant Deposit (FCD) Date

2016-12-22

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