  In this paper we propose that cosmological time is a quantum observable that
does not commute with other quantum operators essential for the definition of
cosmological states, notably the cosmological constant. This is inspired by
properties of a measure of time---the Chern-Simons time---and the fact that in
some theories it appears as a conjugate to the cosmological constant, with the
two promoted to non-commuting quantum operators. Thus, the Universe may be
"delocalised" in time: it does not {\it know} the time, a property which opens
up new cosmological scenarios, as well as invalidating several paradoxes, such
as the timelike tower of turtles associated with an omnipresent time line.
Alternatively, a Universe with a sharply defined clock time must have an
indeterminate cosmological constant. The challenge then is to explain how
islands of localized time may emerge, and give rise to localized histories. In
some scenarios this is achieved by backward transitions in quantum time,
cycling the Universe in something akin to a time machine cycle, with classical
flow and quantum ebbing. The emergence on matter in a sea of Lambda probably
provides the ballast behind classical behaviour.
