  In this article, we investigate various physical implications of quantum
circuit complexity using squeezed state formalism of Primordial Gravitational
Waves (PGW). Recently quantum information theoretic concepts, such as
entanglement entropy, and complexity are playing a pivotal role to understand
the dynamics of quantum system even in the diverse fields such as, high energy
physics and cosmology. This paper is devoted in studying quantum circuit
complexity of PGW for various cosmological models, such as de Sitter,
inflation, radiation, reheating, matter, bouncing, cyclic and black hole gas
model etc. We compute complexity measure using both Covariance and Nielsen's
wave function method for three different choices of quantum initial vacua:
Motta-Allen, $\alpha$ and Bunch-Davies. Besides computing circuit complexity,
we have also computed Von-Neumann entanglement entropy. By making the
comparison of complexity with entanglement entropy, we are able to probe
various features regarding the dynamics of evolution for different cosmological
models. Because entanglement entropy is independent of the squeezing angle, we
are able to understand more details of the system using Nielsen's measure of
complexity which is dependent on both squeezing parameter and angle. This
implies that quantum complexity could indeed be a useful probe to study quantum
features in cosmological scale. Quantum complexity is also becoming a powerful
technique to understand the chaotic behaviour and random fluctuations of
quantum fields. Using the growth of complexity, we are able to compute quantum
Lyapunov exponent for various cosmological models and comment on it's chaotic
nature.
