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arxiv: 1006.5457 · v3 · pith:LCUVWGYInew · submitted 2010-06-28 · 🌌 astro-ph.CO · gr-qc

A new method for calculating the primordial bispectrum in the squeezed limit

classification 🌌 astro-ph.CO gr-qc
keywords bispectrumcreminelliinflationlimitzaldarriagaargumentcalculationconsistency
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In 2004, Creminelli and Zaldarriaga proposed a consistency relation for the primordial curvature perturbation of all single-field inflation models; it related the bispectrum in the squeezed limit to the spectral tilt. We have developed a technique, based in part on the Creminelli and Zaldarriaga argument, that can greatly simplify the calculation of the squeezed-limit bispectrum using the in-in formalism; we were able to arrive at a generic formula that does not rely on a slow-roll approximation. Using our formula, we explicitly tested the consistency relation for power-law inflation and for an exactly scale-invariant model by Starobinsky; for the latter model, Creminelli and Zaldarriaga's argument predicts a vanishing bispectrum whereas our quantum calculation shows a non-zero bispectrum that approaches zero in the long-wavelength limit and for inflation with a large number of e-folds.

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