The Thermodynamic Evolution of the Cosmological Event Horizon |
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| Authors: | Scott Funkhouser |
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| Institution: | (1) SPAWAR Systems Center Atlantic, One Innovation Drive, North Charleston, SC 29406, USA |
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| Abstract: | By manipulating the integral expression for the proper radius R
e
of the cosmological event horizon (CEH) in a Friedmann-Robertson-Walker (FRW) universe we obtain an analytical expression
for the change δR
e
in response to a uniform fluctuation δρ in the average cosmic background density ρ. We stipulate that the fluctuation arises within a vanishing interval of proper time, during which the CEH is approximately
stationary, and evolves subsequently such that δρ/ρ is constant. The respective variations 2πR
e
δR
e
and δE
e
in the horizon entropy S
e
and enclosed energy E
e
should be therefore related through the cosmological Clausius relation. In that manner we find that the temperature T
e
of the CEH at an arbitrary time in a flat FRW universe is E
e
/S
e
, which recovers asymptotically the usual static de Sitter temperature. Furthermore it is proven that during radiation-dominance
and in late times the CEH conforms to the fully dynamical First Law T
e
dS
e
=PdV
e
−dE
e
, where V
e
is the enclosed volume and P is the average cosmic pressure. |
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| Keywords: | |
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