The Primordial Trispectrum Through a Bounce: tauNL and gNL Against the Planck Bound

The four-point function of the primordial perturbations tests the structure of the generating mechanism in ways the bispectrum cannot, because its two standard amplitudes respond differently to single-source and multi-source generation. This paper computes both for perturbations transmitted through a torsion-regulated bounce. The single-source consistency value implied by the local bispectrum is tauNL = 4.72. The direct matching calculation gives a larger value, tauNL = 43.4, because mode mixing across the bounce correlates pairs of modes that a single-source model would leave independent. Both lie far below the Planck bound of 2800, with the direct value a factor 64 under it. The cubic amplitude is gNL = -5215. The gap between the consistency value and the direct value is the informative product: it measures the multi-mode character of bounce generation, and any future trispectrum measurement near the direct value, rather than the consistency value, would identify matching physics rather than a single rolling source as the origin of the perturbations. The study is computed from stated assumptions, not measured.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-11
DOI
https://doi.org/10.5281/zenodo.24134454
Primary Topic
Cosmology and Gravitation Theories
Type
article
Field-Weighted Citation Impact
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article

The Primordial Trispectrum Through a Bounce: tauNL and gNL Against the Planck Bound

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
article

The Primordial Trispectrum Through a Bounce: tauNL and gNL Against the Planck Bound

William Alexander Aldred
article en

Abstract

The four-point function of the primordial perturbations tests the structure of the generating mechanism in ways the bispectrum cannot, because its two standard amplitudes respond differently to single-source and multi-source generation. This paper computes both for perturbations transmitted through a torsion-regulated bounce. The single-source consistency value implied by the local bispectrum is tauNL = 4.72. The direct matching calculation gives a larger value, tauNL = 43.4, because mode mixing across the bounce correlates pairs of modes that a single-source model would leave independent. Both lie far below the Planck bound of 2800, with the direct value a factor 64 under it. The cubic amplitude is gNL = -5215. The gap between the consistency value and the direct value is the informative product: it measures the multi-mode character of bounce generation, and any future trispectrum measurement near the direct value, rather than the consistency value, would identify matching physics rather than a single rolling source as the origin of the perturbations. The study is computed from stated assumptions, not measured.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
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