A tale of three points: mixed and tensor bispectra beyond leading order in Horndeski gravity
Abstract
We derive the primordial ⟨ζζh⟩, ⟨ζhh⟩, and ⟨ hhh⟩ bispectra in general Horndeski theory through first order in slow variation, retaining their complete momentum and helicity dependence. The calculation includes the time evolution of the cubic coefficients, the correction to the scale factor, the first-order scalar and tensor mode functions, and the corrected power-spectrum normalization. We verify the tensor-soft and scalar-soft Maldacena consistency relations at the same order. We also study finite squeezing and show that, when cS≠ cT, the relevant soft variable is the ratio cTq/(cSk), leading to an acoustic crossover not captured by geometric squeezing alone. We construct the corresponding nonlinearity parameters and apply the general results to a nonsingular contracting model, in which the mixed bispectra retain sensitivity to the contraction parameter through the scalar propagation speed.
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BibTeX
@misc{ageeva2026tale,
title = {{A tale of three points: mixed and tensor bispectra beyond leading order in Horndeski gravity}},
author = {Y. A. Ageeva and M. A. Stepanov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30269},
eprint = {2610.30269},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30269},
}
RIS
TY - UNPB
TI - A tale of three points: mixed and tensor bispectra beyond leading order in Horndeski gravity
AU - Y. A. Ageeva
AU - M. A. Stepanov
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30269
UR - https://arxiv.org/abs/2610.30269
AB - We derive the primordial ⟨ζζh⟩, ⟨ζhh⟩, and ⟨ hhh⟩ bispectra in general Horndeski theory through first order in slow variation, retaining their complete momentum and helicity dependence. The calculation includes the time evolution of the cubic coefficients, the correction to the scale factor, the first-order scalar and tensor mode functions, and the corrected power-spectrum normalization. We verify the tensor-soft and scalar-soft Maldacena consistency relations at the same order. We also study finite squeezing and show that, when c_S≠ c_T, the relevant soft variable is the ratio c_Tq/(c_Sk), leading to an acoustic crossover not captured by geometric squeezing alone. We construct the corresponding nonlinearity parameters and apply the general results to a nonsingular contracting model, in which the mixed bispectra retain sensitivity to the contraction parameter through the scalar propagation speed.
ER -