Re: Travesty of big-bang energetics

[David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>]

> > The 1st law of thermodynamics states that the energy in the universe is
> > constant
>
> OK.  We agree on something.  Actually it says more than that, but that's
> good enough for now.

I'm not so sure that even *that* is good enough for now.  Global energy
conservation is not guaranteed (or even objectively definable) in GR--
especially for a metric that is (a) everywhere time dependent, and (b)
not asymptotic to a flat Minkowski metric at 'infinity' for a universe
that has an always a localized distribution of matter.  Unfortunately,
the usual Friedmann-Robertson-Walker metric models for the big bang
satisfy neither a) nor b).  As usual with city politics and GR
everything is local.  Energy is locally conserved in that its density
obeys a relativistic continuity equation.  (Sorry Leigh.)  But this
local conservation law does not always translate into a global
conservation or even coordinate system-independent definability of the
very concept.

Another thing to keep in mind is that when the temperature (kT) is much
higher than the rest energy (m*c^2) of the particles of the matter fields
(as it is in the very early universe) and the system is effectively a
'radiation-like' system that obeys a Planckian-like thermodynamics that
is effectively like the stat mech of pure EM radiation--except for a few
constant multipliers related to the multiplicity of other fields present
besides the EM degrees of freedom, the equation of state (because of the
effectively negligible value of the chemical potentials relative to the
temperature resulting from the freely vigorous particle nonconservation
pair creation/annihilation-type processes) no longer has the same number
of independent thermodynamic parameters (temp, pressure, particle
density, etc.) determining the equilibrium state.  Essentially all the
intensive quantities become determined once the temperature is specified.
The reason for this is essentially that at a high enough temperature the
temperature is the only relevant energy scale in the problem.  Recall
that for Plankian radiation in equilibrium the particle (i.e. photon
number) density, the pressure, the energy density, the entropy density,
the free energy & enthaply densities, etc. *all* are determined once the
temperature is given.  This is in marked contrast to the case where the
temperature is so low that the particle numbers are effectively conserved
as in the ideal gas and similar eqns. of state which require both the
temperature and the particle density to be independently adjustable
parameters which together determine the pressure (p = (N/V)*k*T).

At an early enough stage of the hot big bang cosmic expansion the
temperature is so high that all the other intensive parameters are slaved
to it.  This means that the mass/energy density of the universe is no
longer as separately adjustable parameter from the temperature, and that
as the expansion proceeds energy/matter is everywhere created & destroyed
according to the local dictates of the background temperature and its
behavior is determined by the model.  This is why Guth likes to call the
big bang the "ultimate free lunch".  The net amount of matter created as
the big bang cools depends on the details of the cooling process, the
mass of the Higgs, the number of flavors of various particle types,
CP-violating amplitudes, and a bunch of other model-dependent
quantities.  But the upshot is that the model determines the local
mass/energy density content of space and its expansion rate as space
expands and the system cools.  This is *not* an energy conserving process
and the total amount of energy in the universe is not constant.

David Bowman
dbowman@georgetowncollege.edu