  In this paper, we study the Krylov complexity ($K$) from the
planar/inflationary patch of the de Sitter space using the two mode squeezed
state formalism in the presence of an effective field having sound speed $c_s$.
From our analysis, we obtain the explicit behavior of Krylov complexity ($K$)
and lancoz coefficients ($b_n$) with respect to the conformal time scale and
scale factor in the presence of effective sound speed $c_s$. Since lancoz
coefficients ($b_n$) grow linearly with integer $n$, this suggests that
universe acts like a chaotic system during this period. We also obtain the
corresponding Lyapunov exponent $\lambda$ in presence of effective sound speed
$c_s$. We show that the Krylov complexity ($K$) for this system is equal to
average particle numbers suggesting it's relation to the volume. Finally, we
give a comparison of Krylov complexity ($K$) with entanglement entropy
(Von-Neumann) where we found that there is a large difference between Krylov
complexity ($K$) and entanglement entropy for large values of squeezing
amplitude. This suggests that Krylov complexity ($K$) can be a significant
probe for studying the dynamics of the cosmological system even after the
saturation of entanglement entropy.
