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 \(f(\phi,R)\) modified gravity inflation. We derive the evolution equations for the squeezed strength \(r_k\) and squeezed angle \(\varphi_k\), 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 \(f(\phi,R)\) modified gravity primarily reorganizes the amplitude, phase, complexity, and information loss dynamics of primordial quantum fluctuations.

arXiv:2607.09408 [hep-th]

(or arXiv:2607.09408v3 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2607.09408 Focus to learn more arXiv-issued DOI via DataCite

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