Heat Flow as Origin of Dark Energy

We first introduce entropy according to University Physics textbooks, then, briefly discuss it, and then we prove by a general relativistic derivation that the Universe has entropy growth, like a white-hole, that it is R 2 -dependent, and that dark energy, represented by a cosmological “constant”, is caused by heat flow, and provides for entropy growth.


Introduction
The entropy growth in the Universe was studied by Berman [1]. Here, we re-address the problem. One of the reasons for such return to this subject is that in the latter paper, we considere the absolute temperature to be represented by the Machian temperature, the sort of thing that is problematic, so, now, we conform to standard treatises, where the absolute temperature of the Universe is identified by its radiation, rather than by its matter contents. The better result is that we find either for the Universe or for black holes, the same dependence of entropy, while in reference [1], the non-standard temperature definition, yielded, for the Universe, an entropic formula dependent on 2 -R 3 2 . R However, the main motivation of entropy study is the deficiency of Standard Cosmological theory, whereby the fluid is isentropic, nobody is willing to accept the sort of thing. The entropy of the Universe is a measure of the disorder which entails negative information, according to Claude Shannons in-terpretation in the theory of communication. Berman and Gomide [2] showed that the Universe resembled a Kerr white-hole. Here, we just show that the formula for entropy of the Universe is the same as for a white-hole, i.e., varies with the square of the radius. Then we delve into dark energy considerations showing its physical origin, as heat flow in the Universe.

Entropy in Physics Textbooks
Berman [3] has shown, by pseudotensors, that the total energy of the Universe, is constant zero.
From Thermodynamics, the entropy of a reversible process, is given by [4], where total and stand for absolute temperature, entropy, total energy, pressure and volume.

Entropy of the Universe
According to George F.R. Ellis [5], many statements, about the nature of entropy, are wrong when gravity is dominant, as is the case in Cosmology. Such studies, he says, are ill-founded. We tried to get rid of such inconveniencies, by working directly upon first principles. As the total energy of the Universe, is constant zero, we find, On the other hand, Machian analyses make the energy density dependent on in accordance with Berman [6,7]. The Machian theory, includes the zero-total energy theorem, and includes Brans-Dicke relation, which we take as exact.  [8]. Thus, iv Then the Un ersal entropy v the scale-factor.The Hawking formula for Black-Holes, is also dependent on the surface of the event horizon, ie, it is also R 2 -dependent [9].

Entropy Growth w
In a very popular paper Berman [10], has sho at entropy growth is attained by a cosmological "constant", that represents dark energy, and varies with cosmic time. His result, is given by formula, where the constant  arises from the three-volume of the Universe, when described by, On the other hand, when one deals with R ch ayaudhuris equation, [11], and disconsider shear, and turn into a non-accelerating fluid, we find [12], that the rk energy, which causes the accelera rse, is due to heat flow.

Conclusion
We find that entr cosmological "con physically signifies that there is a positive heat flow in the Universe.

Acknowl
MSB thanks for the importan Solange Lima Kaczyk,now a tinued during the last five years of his research in Cosmology.
, "Entropy Growth in th OConnell and A. Ha Bang-Theory, Assumptions and Problems, Nova Science Publishers, New York, 2012.
[2] M. S. Berman and F. de Mello Gomide, Journal of Modern Physics, to be Published, 2