Inflationary power spectrum from the Lanczos algorithm

• URL: http://arxiv.org/abs/2505.20595v1
• Date: Tue, 27 May 2025 00:10:41 GMT
• Title: Inflationary power spectrum from the Lanczos algorithm
• Authors: Ke-Hong Zhai, Lei-Hua Liu, Hai-Qing Zhang,
• Abstract summary: We obtain an open two-mode squeezed state as the quantum origin for the curvature perturbation.<n>We calculate its corresponding power spectrum by using the Bogoliubov transformation.<n>Our research may offer a new insight into the calculation of the correlation functions through a group-theoretic perspective.
• Score: 1.2152813244704233
• License: http://creativecommons.org/licenses/by/4.0/
• 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 \( \phi_k \). 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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