English

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

Cosmology and Nongalactic Astrophysics 2010-12-21 v3 General Relativity and Quantum Cosmology

Abstract

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.

Cite

@article{arxiv.1006.5457,
  title  = {A new method for calculating the primordial bispectrum in the squeezed limit},
  author = {Jonathan Ganc and Eiichiro Komatsu},
  journal= {arXiv preprint arXiv:1006.5457},
  year   = {2010}
}

Comments

24 pages, 0 figures; v3: added a section calculating the squeezed limit bispectrum of a model by Starobinsky, accepted by JCAP; v2: refocused paper on main result, improved proof of consistency relation, added some references

R2 v1 2026-06-21T15:42:04.870Z