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From: gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>)
Newsgroups: net.physics
Subject: Re: predicting the universe with computers
Message-ID: <7856@brl-tgr.ARPA>
Date: Wed, 30-Jan-85 12:39:23 EST
Article-I.D.: brl-tgr.7856
Posted: Wed Jan 30 12:39:23 1985
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Thanks to Ethan for a good summary of the history of the cosmological term.

> Actually, within standard GR there appears no theoretical reason to discard L
> except those of simplicity.  It may very well be demanded in any case from
> particle physics (although the only 'natural' values are experimentally absurd).

Indeed, the deSitter solution is a highly symmetric one and apparently the
"natural" background space-time when a cosmological term is present.  There
is some relation (not fully known to me) with the "deSitter group", which I
recall was of some interest several years ago in elementary particle theory.

I think the point is sufficiently important that I will repeat it and
elaborate a bit:

	When one produces a unified field theory along the lines of
	the classical development of General Relativity but with
	various symmetry constraints removed, if only ONE field is
	taken as fundamental it has to be the "affine" connection and
	not the metric tensor.  (There are actually several similar
	connections but they're all related.)  Schr"odinger investigated
	such theories in the late 1940s and found that the "pure affine"
	theory produced from a particular variational principle could be
	formulated to look just like Einstein's equation but WITH a
	"cosmological term" automatically appearing.  In my Master's
	thesis I investigated alternative integrands for the variation
	and determined that they all produced either identical results
	or a symmetry-restricted subset (or, in many cases the integral
	variation vanished identically).  The conclusion is that any
	generalization of general relativity along "classical" lines
	based on the affinity as the sole fundamental structure field
	will yield field equations identical in structure to those of
	the Einstein-Straus theory (under a particular choice of gauge)
	and to those of the Einstein-Kaufman reformulation (except for
	an additional term in the Bianchi identity), if the cosmological
	constant is set equal to zero.  The interesting point is that in
	such a theory the cosmological constant arises in such a way
	that it CANNOT be precisely zero; indeed, its numerical value
	may be set to any positive real value by appropriate choice of
	units.  This shows that the constant is an intrinsic measurement
	of SOMETHING in the local space-time structure, and since it is
	a constant therefore of the whole cosmology.  (It is like an
	inverse square of the "size of the universe".)  One of the nice
	features of the pure affine field theory is that the scaling
	argument of C. P. Johnson, Jr. against the E-S-K theories does
	not apply to the pure affine field laws.