AI 中文总结
研究暴胀中修正引力$f(\phi,R)$原初微扰的量子复杂度，通过推导压缩强度和角的演化方程评估电路与克雷洛夫复杂度，发现$f(\phi,R)$耦合增强压缩强度，使克雷洛夫复杂度增长小，电路复杂度演化更明显，为其量子复杂度提供新见解。
AI 中文摘要
在这项工作中，我们研究了暴胀范式中原初曲率微扰的量子复杂度诊断。我们将规范标量场暴胀与修正引力模型$f(\phi,R)$进行比较，重点关注由$\vec{k}$和$-\vec{k}$动量扇区之间的耦合产生的双模压缩态的演化。从曲率微扰的二次作用出发，我们推导了压缩强度$r_k$和压缩角$\phi_k$的演化方程，并用它们来评估电路复杂度和克雷洛夫空间诊断。具体来说，我们在开放系统扩展中计算了克雷洛夫复杂度、克雷洛夫熵、兰佐斯系数$b_n$和有效耗散贡献$c_n$。我们的数值结果表明，$f(\phi,R)$耦合相对于规范标量场暴胀增强了压缩强度。由于双模压缩态的克雷洛夫复杂度直接由平均对数（$K = \sinh^2 r_k$）控制，这种增强导致克雷洛夫复杂度和相关克雷洛夫空间量的增长较小。此外，电路复杂度在$f(\phi,R)$框架中显示出更明显的演化，特别是在视界穿越之后。最终，我们的工作为修正引力$f(\phi,R)$的量子复杂度提供了新的见解。
英文摘要
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 $f(ϕ,R)$.
Comments37 pages, 6 figures
