  Time is a parameter playing a central role in our most fundamental modelling
of natural laws. Relativity theory shows that the comparison of times measured
by different clocks depends on their relative motion and on the strength of the
gravitational field in which they are embedded. In standard cosmology, the time
parameter is the one measured by fundamental clocks (i.e., clocks at rest with
respect to the expanding space). This proper time is assumed to flow at a
constant rate throughout the whole history of the universe. We make the
alternative hypothesis that the rate at which the cosmological time flows
depends on the dynamical state of the universe. In thermodynamics, the arrow of
time is strongly related to the second law, which states that the entropy of an
isolated system will always increase with time or, at best, stay constant.
Hence, we assume that the time measured by fundamental clocks is proportional
to the entropy of the region of the universe that is causally connected to
them. Under that simple assumption, we find it possible to build toy
cosmological models that present an acceleration of their expansion without any
need for dark energy while being spatially closed and finite, avoiding the need
to deal with infinite values.
