Circuit and Krylov complexity of primordial perturbations of modified gravity in inflation
Abstract
Taking canonical scalar field inflation as the reference case, we investigate the circuit and Krylov complexities of primordial curvature perturbations in an f(ϕ,R) modified gravity inflation. We derive the evolution equations for the squeezed strength rk and squeezed angle φk, and calculate the circuit complexity, Krylov complexity, Krylov entropy, Lanczos coefficients, and effective dissipative contribution. Compared with the canonical model, the squeezed strength rk grows more slowly in the modified gravity inflation and continues to exhibit oscillations after horizon exit. Consequently, the spreading in Krylov space is suppressed and modulated through the relation K=sinh2 rk. Modified gravity also changes the squeezed angle, thereby modifying the phase-space correlations and enhancing the oscillatory behavior of the circuit complexity. In the presence of modified gravity effects, information loss is suppressed before horizon exit, whereas it barely affects information loss after horizon exit. For the parameters considered, the Lyapunov exponent and Lanczos coefficients indicate that modified gravity has little effect on the effective degree of quantum chaoticity. These results show that f(ϕ,R) modified gravity primarily reorganizes the amplitude, phase, complexity, and information loss dynamics of primordial quantum fluctuations.
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BibTeX
@misc{li2026circuit,
title = {{Circuit and Krylov complexity of primordial perturbations of modified gravity in inflation}},
author = {Tao Li and Hai-Bing Fu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.09408},
eprint = {2607.09408},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.09408},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Circuit and Krylov complexity of primordial perturbations of modified gravity in inflation
AU - Tao Li
AU - Hai-Bing Fu
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2607.09408
UR - https://arxiv.org/abs/2607.09408
AB - Taking canonical scalar field inflation as the reference case, we investigate the circuit and Krylov complexities of primordial curvature perturbations in an f(ϕ,R) modified gravity inflation. We derive the evolution equations for the squeezed strength r_k and squeezed angle φ_k, and calculate the circuit complexity, Krylov complexity, Krylov entropy, Lanczos coefficients, and effective dissipative contribution. Compared with the canonical model, the squeezed strength r_k grows more slowly in the modified gravity inflation and continues to exhibit oscillations after horizon exit. Consequently, the spreading in Krylov space is suppressed and modulated through the relation K=sinh^2 r_k. Modified gravity also changes the squeezed angle, thereby modifying the phase-space correlations and enhancing the oscillatory behavior of the circuit complexity. In the presence of modified gravity effects, information loss is suppressed before horizon exit, whereas it barely affects information loss after horizon exit. For the parameters considered, the Lyapunov exponent and Lanczos coefficients indicate that modified gravity has little effect on the effective degree of quantum chaoticity. These results show that f(ϕ,R) modified gravity primarily reorganizes the amplitude, phase, complexity, and information loss dynamics of primordial quantum fluctuations.
ER -