Abstract
In this work, the role of a time-varying Newton constant under the scale-dependent approach is investigated in the thermodynamics of the Friedman equations. In particular, we show that the extended Friedman equations can be derived either from equilibrium thermodynamics when the non-matter energy momentum tensor is interpreted as a fluid or from non-equilibrium thermodynamics when an entropy production term, which depends on the time-varying Newton constant, is included. Finally, a comparison between black hole and cosmological thermodynamics in the framework of scale-dependent gravity is briefly discussed.
Highlights
It is well known that the “standard model” of the Universe is based on the Cosmological Principle [1]
Regardless of the approach used to make progress, the relevance of thermodynamics properties in the cosmological context is doubtless. For example, it is well-known that the temperature is proportional to its surface gravity, and the entropy is proportional to its horizon area [34,35]
Kim [37] proved that it is possible to derive the Friedmann equations describing the dynamics of the universe with any spatial curvature by applying the first law of thermodynamics to the apparent horizon of a FRW geometry, and considering that the entropy is given by a quarter of the apparent horizon area
Summary
It is well known that the “standard model” of the Universe is based on the Cosmological Principle [1]. We have a huge variety of cosmological models (see [2] and references therein) They were based on general relativity but, in light of the above-mentioned discrepancies, the community has moved to study cosmological problems taking advantage of alternative models of gravity. For example, it is well-known that the temperature is proportional to its surface gravity (at the black hole horizon), and the entropy is proportional to its horizon area [34,35] Such quantities, and the corresponding black hole mass, obey the first law of thermodynamics [36]. Black hole physics is usually a substantial motivation to tries to understand how the thermodynamics can serves to gets the Einstein’s field equations in a cosmological context. Some concluding remarks are made in the last section
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