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arXiv · 2505.20595

Inflationary power spectrum from the Lanczos algorithm

Ke-Hong Zhai·Lei-Hua Liu·Hai-Qing Zhang
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Abstract

The generalized Lanczos algorithm can provide a universal method for constructing the wave function under the group structure of Hamiltonian. Based on this fact, we obtain an open two-mode squeezed state as the quantum origin for the curvature perturbation. In light of this wave function in the open system, we successfully develop a new method to calculate its corresponding power spectrum by using the Bogoliubov transformation. Unlike traditional approaches, we explicitly retain the Bogoliubov coefficients in terms of the squeezing amplitude \( r_k \) and the squeezing rotation angle \( ϕ_k \). As a result, the power spectrum of the open two-mode squeezed state will match that of the Bunch-Davies vacuum numerically. Furthermore, the derivation of the open two-mode squeezed state relies on the second kind Meixner polynomial (equivalent to the generalized Lanczos algorithm) and the symmetry of the Hamiltonian. Therefore, our research may offer a new insight into the calculation of the correlation functions through a group-theoretic perspective.

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Ke-Hong Zhai, Lei-Hua Liu, Hai-Qing Zhang. 2025-09-15. Inflationary power spectrum from the Lanczos algorithm. https://doi.org/10.1140/epjc%2Fs10052-025-14791-w

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