  Recently in various theoretical works, path-breaking progress has been made
in recovering the well-known Page Curve of an evaporating black hole with
Quantum Extremal Islands, proposed to solve the long-standing black hole
information loss problem related to the unitarity issue. Motivated by this
concept, in this paper, we study cosmological circuit complexity in the
presence (or absence) of Quantum Extremal Islands in the negative (or positive)
Cosmological Constant with radiation in the background of
Friedmann-Lema$\hat{i}$tre-Robertson-Walker (FLRW) space-time i.e the presence
and absence of islands in anti-de Sitter and the de Sitter spacetime having
SO(2, 3) and SO(1, 4) isometries respectively. Without using any explicit
details of any gravity model, we study the behaviour of the circuit complexity
function with respect to the dynamical cosmological solution for the scale
factors for the above-mentioned two situations in FLRW space-time using
squeezed state formalism. By studying the cosmological circuit complexity,
Out-of-Time Ordered Correlators, and entanglement entropy of the modes of the
squeezed state, in different parameter spaces, we conclude the non-universality
of these measures. Their remarkably different features in the different
parameter spaces suggest their dependence on the parameters of the model under
consideration.
