Complexity of non-trivial sound speed in inflation
  In this paper, we study the impact of non-trivial sound on the evolution of
cosmological complexity in inflationary period. The vacuum state of curvature
perturbation could be treated as squeezed states with two modes, characterized
by the two most essential parameters: angle parameter $\phi_k$ and squeezing
parameter $r_k$. Through $Schr\ddot{o}dinger$ equation, one can obtain the
corresponding evolution equation of $\phi_k$ and $r_k$. Subsequently, the
quantum circuit complexity between a squeezed vacuum state and squeezed states
are evaluated in scalar curvature perturbation with a type of non-trivial sound
speed. Our results reveal that the evolution of complexity at early times shows
the rapid solution comparing with $c_S=1$, in which we implement the resonant
sound speed with various values of $\xi$. In these cases, it shows that the
scrambling time will be lagged with non-vanishing $\xi$. Further, our
methodology sheds a new way of distinguishing various cosmological models.
