Constructing an Entropy-Force Model of the Expansion of the Universe Due to Gravitationally Induced Production of Dark Matter

In the framework of entropic cosmology and Prigogine’s gravitational theory about the connection between geometry and matter, providing the production of particles in the cosmological fluid, as well as in the assumption of exchange entropy at the event horizon, a one-liquid model of the evolution of a spatially flat, homogeneous and isotropic Universe is constructed. For its construction the energy conservation equation is derived from the first law of thermodynamics taking into account gravitationally induced creation of matter and exchange energy processes on the visible horizon of the Universe. On the basis of the energy equation and the fundamental Friedman equation describing the expansion of the Universe, modified Friedman–Robertson–Walker equations have been constructed in the context of the entropic formalism, designed for modelling various dynamical aspects of the evolution of the Universe taking into account adiabatic creation of matter. Several forms of exchangeable phenomenological non-extensive entropies associated with the region of the apparent cosmological horizon were used in their derivation. The obtained evolutionary model, consistent with the standard Λ-model for cold dark matter, is intended to describe without introducing new fields the accelerated expansion of the late Universe, providing its cosmological history.