Repulsive gravity IANAP, so feel free to berate me for thinking apocryphal thoughts! Just as magnetism has two charges, in which particles of like-charge repulse and particles of dissimilar charge attract, might gravity have two charges in which particles of like-charge attract and particles of dissimilar charge repulse?
In practice, the state of magnetism means that there is no system composed of many particles in which all particles attract. Rather, there is a net 0 charge if there are equal numbers of each particle type.
My silly theory regarding gravity would mean in practice that there would be two (or more) "clumps" (or universes) in existence, which are racing away from each other. So in our clump (universe) we see only attracting particles, because all the opposing particles have long since separated out and are racing away beyond the boundary of the observable universe. Just like the alien who lands in China and assumes that all humans have slanted eyes, we only observe the attracting particles (or "charge") and disregard the other, unobservable, "charge".
Is there any way to disprove this idea, or like string theory can I go one believing it as it can never be disproved?
Thanks.
 A: There is speculation whether antiparticles like antiprotons have different gravitational interactions than protons. One of the explanations of the predominance of baryons in our universe is similar to you speculation, that an antiuniverse got all the antibaryons.
The question of whether antimatter has also antigravity, or behaves with gravity differently than matter is to be studied with the AEGIS experiment at CERN. 

The primary scientific goal of the AEgIS experiment is the direct  measurement of the Earth’s gravitational acceleration g on antihydrogen. In the first phase of the experiment, a gravity measurement with 1% precision will be carried out by sending an antihydrogen beam through a classical Moire deflectometer coupled to a position sensitive detector.

This will represent the first direct measurement of a difference in a gravitational effect on an antimatter system.
Until then the science fiction possibility you envisage might have a leg to stand on in physics, though I am not holding my breath.
A: Let's start by assuming you believe General Relativity (on the grounds that it has given the right answers every time it's been tested).
There are various ways to get repulsive gravity in GR. The most obvious way is to have matter with a negative mass. See http://en.wikipedia.org/wiki/Negative_mass for a discussion of this. Such matter has never been observed, so I suppose we can't absolutely rule it out. However it seems unlikely. Your example of two "universes" racing away from each other would mean the universe is uneven on large scales, and the observations so far show the universe is basically the same in all directions. In addition you'd have to come up with a mechanism for the positive and negative matter to have separated in the first place.
There are ways to get repulsive gravity that don't require negative mass. For example there appears to be dark energy (http://en.wikipedia.org/wiki/Dark_energy) generating a gravitational repulsion. Also it's widely believed that at very early times the universe underwent a massive expansion, called Inflation (http://en.wikipedia.org/wiki/Inflation_(cosmology) ) due to repulsive gravity.
A: If you wish to pursue your idea in more depth, you may want to examine Sean Carroll's paper in which he speculates that within a larger multiverse (think of big fan-out tree of universes with differing physics) there exists a specific branch that is an anti-universe to ours, one that travels backward in time relative to our universe. His full paper describes the origin of these two-repulsed-in-time universes as an "empty de Sitter phase [in which a] small temperature [fluctuates] into a proto-inflationary configuration [that leads into a] conventional Big-Bang spacetime [with the] same thing happen[ing] in the far past, but with a reversed arrow of time." I know that doesn't sound much like your much simpler charge model, but the outcomes are strikingly similar: Two universes moving away from each other, in Carroll's case along the axis that we perceive as time. I do not know and will not attempt to speculate whether Carroll's idea also leads to gravity repulsion between the contents of those two inverse universes, or if that question even has meaning. (Well, I will offer this speculation: Reversed time certainly could lead to anti-gravity, so...)
And I just have to mention this: Your question caught my attention strongly because I recently drew up a table on how emergent behaviors in large collections of active entities -- that is, of flocks -- could be derived by using a richer variety of charges and charge behaviors than exists in real physics. I used different numbers of unique charges (1, 2, 3, etc.) with different attraction or repulsion values for their groupings (tuples). Your gravity idea was one of the first entries in my table! In my table I had it as a variant of the 2-charge electric force instead of the 1-charge gravity force (and BTW, the strong force is 3-charge). However, it never even occurred to me that a {2-charge, sames-attract, opposites-repel} model might have applicability in real physics! I think it's very cool that you came up with this speculative force symmetry and then applied it to produce a model that ends up surprisingly similar to Sean Carroll's far more mathematically detailed de Sitter based model.
