Circuit and Krylov complexity of primordial perturbations of modified gravity in inflation

Abstract:In this work, we investigate quantum complexity diagnostics of primordial curvature perturbations within the inflationary paradigm. We compare canonical scalar-field inflation with the modified gravity model $f(\phi,R)$, focusing on the evolution of the two-mode squeezed state generated by the coupling between the $\vec{k}$ and $-\vec{k}$ momentum sectors. Starting from the quadratic action for curvature perturbations, we derive the evolution equations for the squeezed strength $r_k$ and squeezed angle $\phi_k$, utilizing them to evaluate both circuit complexity and Krylov-space diagnostics. Specifically, we compute the Krylov complexity, Krylov entropy, Lanczos coefficients $b_n$, and an effective dissipative contribution $c_n$ within an open-system extension. Our numerical results demonstrate that the $f(\phi,R)$ coupling enhances the squeezed strength relative to the canonical scalar field inflation. Since the Krylov complexity of the two-mode squeezed state is directly controlled by the mean pair number ($K=\sinh^2 r_k$), this enhancement leads to a smaller growth in Krylov complexity and related Krylov-space quantities. Furthermore, circuit complexity displays a more pronounced evolution in the $f(\phi,R)$ framework, particularly after the horizon exit regime. Ultimately, our work sheds new light on the quantum complexity of modified gravity $f(\phi,R)$.

arXiv:2607.09408 [hep-th]

(or arXiv:2607.09408v2 [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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