On Saturday, September 14, 2019 at 8:12:34 AM UTC-5, Alan Grayson wrote:
>
> If the early universe, say before the emergence of the CMBR, consisted of
> a random collection of electrons and photons, wouldn't this correspond to a
> *high*, not low entropy? Wouldn't it be analogous to gas with many
> possible states? Yet cosmologists seem hard pressed to explain an initial
> or early state assuming the entropy is low. AG
>
The inflationary manifold has a cosmological constant Λ ≈ (1/cℓ_p)^2, where
c is a number c < 1 and with a value of around 10^{-3} This means Λ ≈
10^{64}m^{-2}, which is to be compared to today's value of Λ ≈
10^{-52}m^{-2}. What is still studied is the process by which this false
vacuum, or false cosmological constant, transitioned to the value today. If
we take the scenario that inflation started at 10^{-36} sec this would mean
there was a transition of sorts from Λ ≈ 10^{64}m^{-2} → 10^{56}m^{-2} and
in one scenario this transitions in a slow role to a lower value and
transitions again to the low value known.
The amount of information in a region bounded by a cosmological horizon
with area A is S ≈ kA/( cℓ_p)^2 = k/c^2 by the Bousso bound. This means a
tiny region bounded by this cosmological horizon only about 10^{-32}m
across had a total entropy of S ≈ k×10^{6} for k = 1.38×10^{-23}j/K. With
this transition this was some 8 orders of magnitude larger. So as a result
the entropy of the earliest universe was quite small.
LC
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