  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 motions 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 cosmological time flows depends
on the global geometric curvature the Universe. Using a simple one-parameter
model for the relation between proper time and curvature, we build a
cosmological model that fits the Type Ia Supernovae data (the best cosmological
standard candles) without the need for dark energy nor probably exotic dark
matter.
