Thermodynamics of the $$R_{\mathrm{h}}=ct$$ Universe: a simplification of cosmic entropy
Fulvio Melia
Abstract
Abstract In the standard model of cosmology, the Universe began its expansion with an anomalously low entropy, which then grew dramatically to much larger values consistent with the physical conditions at decoupling, roughly 380,000 years after the Big Bang. There does not appear to be a viable explanation for this ‘unnatural’ history, other than via the generalized second law of thermodynamics (GSL), in which the entropy of the bulk, $$S_\mathrm{bulk}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>bulk</mml:mi> </mml:msub> </mml:math> , is combined with the entropy of the apparent (or gravitational) horizon, $$S_{\mathrm{h}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>h</mml:mi> </mml:msub> </mml:math> . This is not completely satisfactory either, however, since this approach seems to require an inexplicable equilibrium between the bulk and horizon temperatures. In this paper, we explore the thermodynamics of an alternative cosmology known as the $$R_{\mathrm{h}}=ct$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>h</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>c</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> universe, which has thus far been highly successful in resolving many other problems or inconsistencies in $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM. We find that $$S_{\mathrm{bulk}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>bulk</mml:mi> </mml:msub> </mml:math> is constant in this model, eliminating the so-called initial entropy problem simply and elegantly. The GSL may still be relevant, however, principally in selecting the arrow of time, given that $$S_{\mathrm{h}}\propto t^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>h</mml:mi> </mml:msub> <mml:mo>∝</mml:mo> <mml:msup> <mml:mi>t</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> in this model.