I was thinking about this "dark energy" and "dark matter" astronomers are
chasing.  It seems like a kludge to fill the gap between our equations and
observation.  Gravity should be causing the universe to accellerate
inward, but yet observation shows it is accellerating outward.  Dark
energy is the common name for the discrepancy.

But what if it's all gravity, just that it doesn't work the way we assume
at large distances?  The 1/r**2 relationship between gravity and distance
appears accurate over our solar system.  There things move fast enough
relative to our distance from them that we can measure their motion from
direct observation over time.  At large distances I know we can measure
the radial velocity from the red/blue shift of known spectral lines, but
do we have a way of measuring accelleration directly?  How much of our
accelleration assumption of distant objects is based on the assumption
that gravity follows 1/r**2?  We can see that gravity is holding galaxies
together, and apparently holding clusters and super clusters of galaxies
together, but how do we really know it works beyond that?  Even if we can
see gravity has a attractive effect on the range of a supercluster of
galaxies, do we have any independent way of mearuring the accelleration of
the galaxies we assume are gravitaionally bound to make quantitative
measurements of gravity at large distances?  I'm really asking since I
don't know.  I have never heard of independent verification of 1/r**2 of
gravity at large distances, but that of course doesn't mean it's not
there.

A simple 2D analogy often used to explain gravity is a streched rubber
sheet.  You put a ball bearing on the sheet, and it makes a depression
such that other smaller things roll towards the ball bearing.  In this
analogy, gravity is strongest nearest the mass causing it, and extends to
infinity as a ever weaker attractive force.

But what if a water bed is a better analogy?  In other words, it's a
zero-sum game in the long run.  It still makes the same depression locally
that follows the familiar 1/r**2 law, but that turns out to be a
approximation that is good only for the small distances we have been able
to measure gravity over.  Eventually it flips over to become a repulsive
force (the average level of the water bed is always the same, if you push
down one place, other places go up to maintain the global average) at
large distances before tailing off.  Or it could do any number of other
things while still following 1/r**2 closely enough over the relatively
small distances where we have observed it to be so.

This is the same kind of concept as Netwon's laws being very good
approximations as long as you stay well below the speed of light.
Newton's laws worked well enough for what we could observe directly in our
solar system.  What if gravity is like that too, where 1/r**2 is a good
approximation for small distances but other parts of the real equation
dominate at large distance?  Do we have any observations that tell us it
doesn't?  As far as I know, accellerations of distant objects is deduced
from gravity, not independently measured, so that's obviously no way to
check gravity itself.

Are there thought experiments we can perform much like what Einstein did
to deduce relativity without direct observation?  What assumptions could
be made, like Einstein's speed of light is constant for all observers,
about gravity to perform such thought experiments?

Does anyone know of any accessible papers that talk about this stuff in
terms someone who doesn't have a PhD in astrophysics can understand?  I'm
sure this has all been thought of and dismissed before, but I'm curios now
and would like to delve into the reasons a bit more.  When I look up stuff
like this I either find nothing (gravity is simply assumed to be 1/r**2
and everything based on that) or the stuff is way over my head so I have
no idea what it's saying.


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