Cosmological Complexity in K-essence

Abstract: We calculate the cosmological complexity under the framework of scalar curvature perturbations for a K-essence model with constant potential. In particular, the squeezed quantum states are defined by acting a two-mode squeezed operator which is characterized by squeezing parameters $r_k$ and $\phi_k$ on vacuum state. The evolution of these squeezing parameters are governed by the $Schr\ddot{o}dinger$ equation, in which the Hamiltonian operator is derived from the cosmological perturbative action. With aid of the solutions of $r_k$ and $\phi_k$, one can calculate the quantum circuit complexity between unsqueezed vacuum state and squeezed quantum states via the wave-function approach. One advantage of K-essence is that it allows us to explore the effects of varied sound speeds on evolution of cosmological complexity. Besides, this model also provides a way for us to distinguish the different cosmological phases by extracting some basic informations, like the scrambling time and Lyapunov exponent etc, from the evolution of cosmological complexity.