I have tried to be as brief and untechnical as possible in the hope that more people will read this. The cost has been some simplification and lack of precision which I hope you can tolerate.
A quantum theory of gravity has been sought in the hope of achieving two goals:
1) unifying gravity with the other three forces of physics.
2) combining quantum theory with general relativity.
Graviton theory has attempted to achieve the first goal. While on the one hand it doesn't work on the other hand it is hard to see how it would achieve the second goal.
An alternative approach is to to consider how a quantum theory of gravity might look in order to be compatible with relativity. Instead of an exchange of virtual particles between massive objects, consider virtual particles from space being absorbed by massive objects. To do this what is first needed is a quantum description of space compatible with the expanding universe.
The result replaces the idea of motion through space with the idea that motion is due to to the expansion and contraction of space. Relativity's curvature of space is described by saying that size of a volume of space with given external dimensions will be smaller if it contains mass.
The conjecture is that space is defined by pairs of virtual Higgs Bosons, that is :- there is a number n such that:
n pairs of virtual Higgs Bosons = one cubic meter of empty space.
Couple this with the vacuum expectation and we have a description of space which can maintain its own expansion.
Imagine an expanding universe without any matter in it, where space is as described above. Because of the expansion, at any instant there is more space than at the previous instant so this will give rise to more virtual particles, which means more space in the next instant. Once it has started to expand the expansion is self sustaining. By the same line of reasoning - if the universe were set contracting then the contraction would be self sustaining - no gravitating matter necessary. The same principle can be applied to any chosen volume of space.
The role of gravity as a property of massive objects is to simply reduce space. Mass either absorbs the pairs of virtual Higgs Bosons or causes them to annihilate each other sooner than they otherwise would. The picture is one of deep space full of nozzles emitting more space into the great void and massive objects as vacuum cleaners sucking up space.
To give an idea of how this works: imagine space divided up into cubes. In one of the cubes is a star sucking up space. That cube will still be touching its neighbours exactly like all the other cubes, only it will contain less space. Effectively the cube with the star in it will be smaller on the inside than it is on the outside. This may sound a little hard to swallow but if you allow that the space around a gravitating body is curved (ie non Euclidean) then a cube of edge say 1 light year will not contain 1 cubic light year of space.
The mechanics of how this works is as follows. Consider the boundary between the star filled cube and its neighbour to the right. There is less space and therefore less virtual Higgs Bosons to the left of the boundary so more Higgs bosons will cross from right to left than from left to right. The more the cube with the star shrinks the faster space from its neighbours flows in. It will shrink to the size such that the net inflow (from neighbouring cubes) of virtual Higgs bosons per second equals the rate at which the star is absorbing them. Its external dimensions will remain unchanged (because that's the way they have been defined) The effect is that all the neighbouring cubes will shrink a little - ie they will become a little smaller on the inside than they are on the outside ( as they lose space to the cube with the star). The effect will propagate outwards loosing strength in accordance with the inverse square law.
To explain a little more the concept of being smaller on the inside than on the outside let's look at how we can now describe a black hole. It is a property of any mass that it swallows space at a given rate. To do this a black hole must have an event horizon big enough to allow sufficient space to pass into the black hole each second (sufficient to feed its appetite). The conventional description of the inside of the event horizon is of empty space with a singularity at the centre. If we allow the space inside the event horizon to be smaller than its external dimensions then there is no need for there to be anything except the singularity inside. Indeed as the space is absorbed at the horizon there can be no space inside. This is consistant with and gives a physical description of relativity's infinite curvature of space.
Take two photons approaching the event horizon at say the north and south poles. From our point of view the two photons are significantly spatially separated. The two points from which they emerge inside the event horizon are not spatially separated - they are the same point - the singularity. The event horizon has a surface area on the outside. You could use Euclidian geometry to calculate its volume. But on the inside it has no volume at all. The event horizon is a boundary of the universe, the dimensions of space and time end there. There is no space on the other side, just as there is no space into which the expanding universe is expanding.
The idea of an object moving through space is replaced by the description that an object moves from A to B by decreasing (absorbing) the space between itself and B while increasing (emitting) space between itself and A. Give the object a push and the space between it and B starts to decrease. Once the space starts to decrease (contract) it will continue to do so as described above in the quantum description of space. One can now replace 'a body continues in a state of rest or uniform motion' with 'a volume of space remains constant or constantly expands or contracts'. You may object here on the grounds that recent observation sugests that the universe is expanding more rapidly lately, this point is addressed in the post script.
I put forward these ideas in the hope that they meet the criteria of a theory in being simple, elegant and in agreement with observation.
With regard to just how the universe is expanding:
instead of saying that an expanding space will continue to expand, one could just as easily say that if the expansion is increasining it will continue to increase or that if the increase in the rate of expansion is increasing then that will continue to increase. Ideally it would just be a matter of finding the polynomial which fits observation, unfortunately we don't have enough observation. On the bright side one can hope that the maths can be derived by the quantum physicists.
Pairs of virtual partices of all kinds pop up in empty space all the time. One of the pair has positive energy and the other negative energy. Effectively they are said to borrow the energy from the vacuum and must quickly annihilate each other to pay back the loan. This is a consequence of the uncertainty principal which in this instace prohibits the vacuum from having exactly zero energy. Back.