2026/07/10 by Tao Li, Hai-Bing Fu
#hep-th #gr-qc #quant-ph
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 k and -k momentum sectors. Starting from the quadratic action for curvature perturbations, we derive the evolution equations for the squeezed strength rk and squeezed angle ϕk, utilizing them to evaluate both circuit complexity and Krylov-space diagnostics. Specifically, we compute the Krylov complexity, Krylov entropy, Lanczos coefficients bn, and an effective dissipative contribution cn 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=\sinh2 rk), 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).