Abstract
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.
Highlights
Since its introduction nearly a century ago [1], general relativity (GR) has been brilliantly confirmed by a number of observations, most notably the perihelion precession of Mercury, the gravitational redshift, and the deflection of light by massive bodies
GR has been used in cosmology to describe the evolution of the universe as a whole, and the model that currently gives the best description of its large-scale structure and evolution (namely, the lambda cold dark matter (ΛCDM) model) is based on the equations of GR
Additional ingredients are necessary to bring the models into agreement with observations dealing with very large scales and very long-term phenomena
Summary
Since its introduction nearly a century ago [1], general relativity (GR) has been brilliantly confirmed by a number of observations, most notably the perihelion precession of Mercury, the gravitational redshift, and the deflection of light by massive bodies. Additional ingredients (dark matter and dark energy) are necessary to bring the models into agreement with observations dealing with very large scales and very long-term phenomena. Emergent gravity [4] was introduced in the context of string theories Starting from this assumption, we develop a very simple, semi-empirical, and mathematically basic toy model of our universe. Other mathematical dependences between time and entropy or between time and a parameter characterising the dynamical state of the universe (such as its curvature or its density parameters, for example) might be proposed or—even better—derived from theoretical considerations.
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