Exact Solutions for Chiral Gravitational Waves from Spin-2 Mixing
Abstract
A spectator spin-2 field can mix linearly with the metric tensor perturbations. We study the coupled tensor system in an inflationary background, including a parity violating effect parametrised by θ. Without expanding in the linear mixing between the two fields, we solve the system exactly for arbitrary mass while treating the mixing strength nonperturbatively. The mode functions of both helicities are constructed by acting with an operator-valued Gauss hypergeometric function 2F1 on Whittaker modes, and the late-time power spectrum of each graviton helicity is expressed in closed form in terms of the generalised hypergeometric function 3F2. We find that one helicity is exponentially enhanced, showing that strong mixing with a spectator spin-2 field can generate a large and highly chiral primordial gravitational wave spectrum. The degree of circular polarisation is bounded by tanh(πθ), independently of the spin-2 mass and the mixing strength. The same solution also gives the late-time power spectrum of the spectator field and its cross spectrum with the graviton. In the weak mixing limit, our exact result reproduces the perturbative Schwinger-Keldysh result. These solutions provide a nonperturbative framework for studying primordial gravitational waves sourced by additional tensor modes.
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BibTeX
@misc{gorji2026exact,
title = {{Exact Solutions for Chiral Gravitational Waves from Spin-2 Mixing}},
author = {Mohammad Ali Gorji and Yuhang Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32571},
eprint = {2609.32571},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32571},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact Solutions for Chiral Gravitational Waves from Spin-2 Mixing
AU - Mohammad Ali Gorji
AU - Yuhang Zhu
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32571
UR - https://arxiv.org/abs/2609.32571
AB - A spectator spin-2 field can mix linearly with the metric tensor perturbations. We study the coupled tensor system in an inflationary background, including a parity violating effect parametrised by θ. Without expanding in the linear mixing between the two fields, we solve the system exactly for arbitrary mass while treating the mixing strength nonperturbatively. The mode functions of both helicities are constructed by acting with an operator-valued Gauss hypergeometric function _2F_1 on Whittaker modes, and the late-time power spectrum of each graviton helicity is expressed in closed form in terms of the generalised hypergeometric function _3F_2. We find that one helicity is exponentially enhanced, showing that strong mixing with a spectator spin-2 field can generate a large and highly chiral primordial gravitational wave spectrum. The degree of circular polarisation is bounded by tanh(πθ), independently of the spin-2 mass and the mixing strength. The same solution also gives the late-time power spectrum of the spectator field and its cross spectrum with the graviton. In the weak mixing limit, our exact result reproduces the perturbative Schwinger-Keldysh result. These solutions provide a nonperturbative framework for studying primordial gravitational waves sourced by additional tensor modes.
ER -