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

• URL: http://arxiv.org/abs/2607.09408v2
• Date: Fri, 17 Jul 2026 06:36:54 GMT
• Title: Circuit and Krylov complexity of primordial perturbations of modified gravity in inflation
• Abstract summary: We compute the Krylov complexity, Krylov entropy, Lanczos coefficients $b_n$, and an effective dissipative contribution $c_n$ within an open-system extension.<n>Our numerical results demonstrate that the $f(,R)$ coupling enhances the squeezed strength relative to the canonical scalar field inflation.<n> circuit complexity displays a more pronounced evolution in the $f(,R)$ framework, particularly after the horizon exit regime.
• Score: 3.3370372705390228
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $f(φ,R)$, 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 $φ_k$, 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 $f(φ,R)$ 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 $f(φ,R)$ framework, particularly after the horizon exit regime. Ultimately, our work sheds new light on the quantum complexity of modified gravity $f(φ,R)$.

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