Dear John,
Your question confuses me as I cannot quite make out what your
conceptual grasp of the notion of expanding space is. The volume of
space between clusters of galaxies on large scales increases with time. That
is what we mean by space expanding. The problems you say this introduces
- of homogeneity and isotropic expansion - are not problems at all.
The standard model has an exactly homogeneous isotropic expansion as
described by an FLRW metric. My proposal alters that by the observation
that homogeneity is only true statistically on scales of at least of order
100/h Mpc, and we have to deal with large variances in geometry and
perceived expansion rates below that scale. Statistically on large
scales there is still homogeneous isotropic expansion.
When you say homogeneity and isotropy are problems, and then mention
inflation, I think you are getting confused with the horizon and flatness
problems, which are quite different issues and have nothing to do with
the overall conceptual notion of expanding space. The horizon and flatness
problems arise because in a standard FLRW model with only matter and
radiation as sources, the past history of the universe before the time
of last-scattering is such that points on our CMB sky which are further apart
than about one degree cannot have been in causal contact before the epoch
of last scattering, once you calculate the volume of their past light cones
at that time. However, the evidence of the CMB
radiation is that the universe was at thermal equilibrium with a near
perfect blackbody spectrum at that time, an impossibility if regions more
than one degree apart had not been able to talk to each other. The
inflationary universe scenario has been invented to solve conundrums such as
the horizon problem I have just described. It has nothing to do with the
notion of expansion of space per se; it just means the relative expansion
rate would have been many orders of magnitude faster very early on, changing
the shape of the past light cones in a dramatic fashion that solves the
horizon problem etc.
The rate of expansion of the universe has nothing
to do with the speed of light per se. The speed of light in vacuum enters
relativity as a fixed universal constant, and the whole of spacetime
structure in Einstein's theory depends on the speed of light being
constant. That means we can always choose a local inertial frame at
a point, which is a Minkowski space. The constancy of the speed of
light is built into the physical structure of this Minkowski space. General
relativity is a larger theory in which spacetime overall can bend
and warp, so that the relative calibration of clocks and rods in
widely separated local Minkowski frames can differ markedly, in a manner
than depends on solutions of Einstein's equations. The Cosmological
Equivalence Principle I have introduced is a means of clarifying
the problem of the relative calibration of clocks of widely separated
frames on cosmological scales in the absence of
exact symmetries of the background - a problem which otherwise has no general
solution in general relativity. I believe I do this in a manner which
naturally incorporates an aspect of Mach's principle, consistent
with the rest of the conceptual foundations of general relativity.
It is dangerous to take the "rubber sheet" analogy too far. Empty
space does not have a fabric, and light can never be brought to rest
in any frame - so you should never talk about space "carrying light
along with it". The fact is that in general relativity the laws of
geometry are not Euclidean but pseudo-Riemannian, and the spatial
relationship of objects are dynamical so the curved geometry changes
over time. That's all there is to the "rubber sheet" or the "fabric"
of space. It is just an analogy for us to be able to conceptualise
curved geometries. But the curvature of the geometry is determined
by matter - matter tells the geometry how to curve and the curved
geometry tells matter how to move - so ultimately it is matter telling
matter how to move via the rules of Einstein's equations, and light moving
in this background is part of the matter in the game; light being
matter which can never be
be brought to rest relative to other matter. If you just think of expanding space as being that the distances and
volume of space between distant galaxies is getting larger, then you
will never go wrong. I think your confusions may arise from taking the rubber sheet too
literally. Whatever started the matter rushing apart in a particular
manner at the earliest fractions of a second of existence is something
beyond the laws of general relativity, and part of physics still to be
determined, maybe in quantum gravity. Inflationary models have such properties but depend highly on even earlier initial conditions within their parameter space; and there are hundreds of models of inflation. I regard them as phenomenological decriptions which fit the observations, but do not deserve to be called a fundamental theory until some genuine theoretical insight that has yet to be made picks out some scenario in a compelling fashion, and rules others out. Anyway given initial conditions at the time of last scattering or earlier in the radiation-dominated era,
once the laws of physics as we understand them held sway ordinary matter
will decelerate the expansion rate in a manner consistent with Einstein's
equations.
Finally when you say "there doesn't appear any other reason for redshift
than a form of recessional velocity", that is not correct. Redshift just
arises in comparing the relative frequency of a photon at the emitter
and at an observer's position, and these can change in general relativity
due to a relative calibration of the clocks of those two frames in many
ways. Here are three ways: (i) cosmological redshift - the overall volume
of space has increased; (ii) peculiar velocity redshift - there is
a local boost of the emitter and/or observer frame relative to the overall
cosmological expansion; (iii) gravitational redshift - the relative
distribution of matter between source and emitter and resulting gravitational
"potentials" induces other relative changes of frequency over and above the
first two effects. Now it is true that general relativity is a theory in
which we cannot *locally* distinguish these different types of redshifts,
but that is quite different than your statement.
The Cosmological Equivalence Principle extends the range of these equivalent
circumstances. In particular, even though it is an old textbook statement
that the redshift in a FLRW universe is *locally* equivalent to a peculiar
velocity in Minkowski space, the CEP states that even though the universe
is inhomogeneous - so the FLRW models are not globally valid - nonetheless
regional frames can always be found for arbitrarily long periods during
which the average decelerating volume expansion is conformally equivalent
to a Minkowski frame, and therefore with volume expansion which is
indistinguishable from the equivalent motion of a congruence of particles
in a static Minkowski space by the standard textbook argument. Furthermore,
I establish a new type of gravitational time dilation and gravitational
redshift. We are used to thinking about static gravitational potentials
and the equivalence of a static observer in such a potential (eg someone
at the Earth's surface) with an observer firing rockets. I introduce a
different notion of gravitational time dilation due to cumulative variations
of dynamically varying "potentials". This is to be thought of as relative
deceleration of the expanding average background due to gravity being
equivalent to a regional homogeneous/isotropic symmetry-preserving
deceleration of a tethered lattice of observers in Minkowski space.