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arXiv · 2610.30269

A tale of three points: mixed and tensor bispectra beyond leading order in Horndeski gravity

Y. A. Ageeva·M. A. Stepanov
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Abstract

We derive the primordial $\langleζζh\rangle$, $\langleζhh\rangle$, and $\langle hhh\rangle$ 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 $c_S\neq c_T$, 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.

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Y. A. Ageeva, M. A. Stepanov. 2026-10-21. A tale of three points: mixed and tensor bispectra beyond leading order in Horndeski gravity. https://arxiv.org/abs/2610.30269

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