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