  We examine the holographic complexity conjectures in the context of
holographic theories of FRW spacetimes. Analyzing first the complexity-action
conjecture for a flat FRW universe with one component, we find that the
complexity grows as $t^2$, regardless of the value of $w$. In addition, we
examine the holographic complexity for a flat universe sourced by a scalar
field that is undergoing a transition. We find that the complexity decreases
when the holographic entanglement entropy decreases for this universe.
Moreover, the calculations show that, while the entanglement entropy decreases
only slightly, the magnitudes of the corresponding fractional decreases in
complexity are much larger. This presumably reflects the fact that entanglement
is computationally expensive. Interestingly, we find that the gravitational
action behaves like a complexity, while the total action is negative, and is
thus ill-suited as a measure of complexity, in contrast to the conjectures in
AdS settings. Finally, the implications of the complexity-volume conjecture are
examined. The results are qualitatively similar to the complexity-action
conjecture.
