kodama said:
the news media has published the fact that there has thus far been no detection of gravitational waves as predicted by GR. eg Parkes Pulsar Timing Array found nothing after 11 years.
If there are no gravitational waves, then GR is wrong. a common argument for gravitons is that there are gravitational waves so there must be gravitons due to wave particle duality
how would gravity, GR, strings, loops, QG be modified if there are no gravitational waves as the non-detection thus far have found?
are there any alternative gravity theories that pass all tests of classical GR but no gravitational waves?
Absence of evidence isn't strong evidence of absence. Gravitational waves should be subtle and I haven't seen any really solid theoretical predictions that existing instrumentation would definitely be able to detect them. The theoretically predicted signal is extremely faint in most circumstances. To disprove a theory you need not just non-detection of a signal, but a clear theoretical prediction from the theory that you would have seen the signal.
At this point, we are in a similar situation to 16th century astronomers who had not yet discovered galaxies. They had primitive instrumentation that could see more than the naked eye, but nothing sufficiently powerful to see a galaxy for what it was, even if they had known that they were predicted.
The main reason that the gravitational waves are so hard to see is that gravity is so weak relative to the three SM forces (electromagnetism, weak force and strong force) and operate at huge distances and require immense masses to generate significant gravitational forces. Thus, we can't experimentally move huge masses in a sudden way for significant distances as we would need to in order to observe gravitational waves that disrupt the background much. Instead, we have to look for places in the universe where something like that might be happening and measure that very precisely. As another analogy, it is like trying to see waves of water in some place where the water is still because there are no tides and no wind with a nearsighted naked eye.
One of the fundamental differences between GR and Newtonian gravity is that gravity propagates at the speed of light, rather than instantaneously. In the absence of a mechanism by which gravity propagates at the speed of light rather than instantly, the causal structure of the laws of the universe would break down as tachyonic gravity propagation conveyed information outside of light cones to the entire universe at once. This could be a real mess and there is certainly no evidence for tachyonic gravity. The apparently finite age of the universe is one reason among many that indirectly suggests that gravity propagates at a finite speed rather than instantaneously.
One of the reasons for predicting waves or gravitons, rather than, for example, straight line rays, is that in addition to direction, one also needs to know the strength of a gravitational pull and the frequency of the wave provides a degree of freedom in which to embed that information, and because the wave/bosonic particle duality model works for all of the other forces in Nature and physicists aren't all that original. But, GR doesn't say much about the frequency of gravitational waves (as far as I know this is still an unsolved issue upon which there are competing views although I would welcome corrections from anyone who knows better), which also makes it harder to know what you are looking for.
One could image that gravity fairies or gravity mosquitoes instead of waves or gravitons carried the gravitational force, but one would expect them to act pretty much like hypothetical gravitons in order to match precision solar system observations and other astronomy observations, so that might be a distinction without a difference.
There is serious investigation of the possibility that gravity may be conveyed not by a massless spin-2 graviton, but by a spin-2 graviton with infinitessimal mass, which is called "massive gravity" and would imply among other things, that gravitons, like neutrinos, propagate extremely fast, but not quite at the speed of light. (There are other consequences too).
While both string theory and LQG don't rule out trajectories of particles (bosons or fermions) that seem non-local, in both cases this is possible in theory only because the topology of space-time may not be as continuous, smooth and local as it seems and may have points that are connected to other points that we perceive as non-local, either via a wormhole or the emergent nature of locality, when they really aren't (the book "A Wrinkle In Time" talks about this concept in language an elementary school student can understand). Neither predicts the instant propagation of gravitational signals.
QG is a kind of theory, not a particular theory, so it doesn't predict anything, but any theory modeled on quantum mechanics is going to adopt Lorenz invariance, which pretty much implies gravitational waves, as a fundamental law just as it is in other aspects of quantum mechanics.
