Physical theory which matches MOND results

I'm on a couple of weeks leave from my computing job at the
moment and I've been using the time to do some physics again.
I've found that one of my old ideas gives the same result as the
successful but purely empirical MOND theory which explains galaxy
rotation curves, but derives it from a simple physical
hypothesis. I've currently posted about it to the moderated
newsgroup sci.physics.research and also e-mailed a copy to Prof.
Milgrom, the author of the MOND theory, but it would be nice to
discuss it with someone before I run out of leave (even if only
to shoot it down so I can start thinking about something else).
Perhaps to do it properly I should submit a letter to some
journal, but if this is already known about that would be a
waste of time, especially as I don't know where to start.

Here are the details of the idea (which I hope is sufficiently
specific and testable to call a "theory"):

In local GR calculations, one normally assumes that space is flat
at a sufficient distance from the local mass or masses which are
being studied. However, if the local mass m constitutes a
significant fraction m/M of the total mass of the universe, then
this assumption seems questionable. If the universe is spatially
finite at a given moment in time, then a more plausible
assumption would be that the region containing a fraction m/M of
the total mass would also loosely speaking contain a related
fraction of the 3D "angle" needed to close the universe, so the
limit would be "conical" rather than "flat".

More specifically, a starting hypothesis might be that a sphere
enclosing a fraction m/M of the total mass of the universe would
effectively be slightly "conical", missing that proportion of its
surface area at any given radius, in the same way that a 2D cone
made out of paper has a fixed proportion of its circumference
missing at a given radius. For the 3D case, this would mean that
the effective radius of the sphere was reduced by a factor
sqrt(1-m/M). This factor is then the cosine of the angle by
which the "cone" diverges from flat space, so the sine of the
angle is sqrt(m/M) and this also then gives the angle of deviation
from flatness in radians.

The conical space-time at distance r from the source is then
curved by 1/r sqrt(m/M) so bodies moving through that
space-time would appear to be accelerated by an extra
gravitational acceleration c**2/r sqrt(m/M).

In MOND, the extra acceleration is sqrt(G m a0)/r where a0 is
an arbitrary constant set to be approximately 1.2e-10 ms**-2 to
fit the experimental results. For our hypothesis to match MOND
exactly, we only require that M is equal to (c**4 / G a0),
which gives a value of approximately 10**54 kg. Although
trivial methods of estimating the mass of the universe give a
result a little lower, around 3 * 10**52 kg, this seems to me
to be an interestingly close fit. This suggests that the
existing MOND acceleration term could perhaps be written
instead as c**2/r sqrt(m/M), where M is around 10**54 kg and
may well correspond in some sense to the total mass of the
universe, and that it might be possible to find a way to relate
this physically to a "conical" limit instead of a "flat" limit
in gravitational calculations.

I must admit to some use of "analogies" rather than formal
calculations in the way that I get from the cone angle being
sqrt(m/M) to the space-time curvature being 1/r times that and
hence the acceleration being c**2 times the curvature. I'm
also not a professional physicist but as it is possible for
readers to check out everything I've said for themselves
that should not have any bearing on the value of the results.

The "conical" model might also help how to analyze cases where
more than one mass is involved. In particular, it seems that as
the conical model effectively creates the large-scale curvature
of the universe out of conical distortions surrounding individual
masses, then these conical effects may not necessarily be
spherically symmetrical, which might give rise to possible
testable differences from the original MOND theory.

Jonathan Scott