<i>C</i> ausality <i>C</i> onstraint on <i>C</i> ircuit <i>C</i> omplexity from <i>COSMOEFT</i>

In this article, we investigate the physical implications of causality constraint via effective sound speed $c_s(\leq 1)$ on Quantum Circuit Complexity(QCC) in framework Cosmological Effective Field Theory (COSMOEFT) using two-mode squeezed quantum states. This COSMOEFT setup is constructed St$\ddot{\text{u}}$ckelberg trick with help lowest dimensional operators, which are broken under time diffeomorphism. setup, consider only contribution from two derivative terms background quasi de Sitter metric. Next, compute relevant measures circuit complexity and their cosmological evolution for different $c_s$ by following approaches, Nielsen's Covariance matrix method. Using also Von-Neumann R\'enyi entropy, finally establishes an underlying connecting relationship between entanglement entropy complexity. Essentially, study behaviour respect to scale factor find various interesting unexplored features within window, $0.024\leq c_s\leq 1$, supported both observation. Finally, comment connection complexity, equilibrium temperature lying mentioned window.