Constructing an Entropic-Force Model for the Expansion of the Universe Caused by Gravitationally-Induced Production of Dark Matter

In the framework of entropic cosmology and Prigogine’s gravitational theory on the link between geometry and matter, providing the production of particles in the cosmological fluid, as well as under the assumption of exchange entropy at the event horizon, a one-liquid model of the evolution of a spatially flat, homogeneous, and isotropic Universe has been developed. To construct it, the energy conservation equation was derived from the first law of thermodynamics by accounting for the gravitationally-induced creation of matter and the exchange energy processes on the apparent horizon of the Universe. On the basis of this equation and the fundamental Friedmann equation describing the expansion of the Universe, as well as in the entropic formalism context, we constructed the modified Friedmann–Robertson–Walker equations that can be used to study various dynamical aspects of the evolution of the Universe with adiabatic creation of matter. When deriving them, we used several forms of exchangeable phenomenological entropies associated with the region of the apparent cosmological horizon.