In my informed, but not necessarily expert, opinion, the most promising work on quantum gravity in the world today (so far) has been done by Alexandre Deur, and I've devoted a permanent page
on this blog discussing this work. I think that it is more likely than not the case that this approach is the correct one to explaining quantum gravity.
In a nutshell, this approach to quantum gravity explains dark matter and dark energy as second order quantum gravity effects that are ignored in general relativity that arise from proper consideration of the self-interactions of gravitons. Dark matter is viewed as the excess concentration of gravitons in places where matter is at the expense of gravitons going in other directions due to their self-interaction. Dark energy flows from gravitons partially staying within gravitational systems like galaxies which reduces the flow of gravitons between gravitational systems thereby reducing the gravitational pull of those systems to each other - thus, dark energy phenomena arise because the gravitational pull between systems is weakened, not because something else is pulling these systems apart from each other.
To be clear, I am not saying that Deur's approach to quantum gravity has been rigorously confirmed, although several of his articles have been published in peer reviewed journals.
But, I am saying that he is doing something that no one else in the quantum gravity field is doing, and that his approach is the most promising one that has been proposed by anyone to solve several of the most important unsolved question in physics that are outstanding today, and it does so simultaneously.
Also, even if he isn't 100% correct, many of the ideas that make up the entire package of its ideas deserve more attention and may provide a basis for advances even if other parts of this package of ideas don't pan out.
Why should you consider my opinion?
I read the abstracts of almost every astronomy, general relativity, high energy physics experiment, high energy physics lattice, and high energy physics phenomenology preprint on arXiv and have done so reasonably (although not perfectly) consistently since I started this blog more than eight years ago, and I go deeper and read some or all of the body text of several of those articles almost every week day. I also follow all of the physics blogs shown in the sidebar on a regular basis, and have done additional research on things I don't understand or want to know more about from secondary sources on the web, hard copy physics books oriented towards educated laymen, and math and physics textbooks in hard copy (some of which go beyond what I studied as an undergraduate college student).
I don't have the depth of knowledge of a PhD in physics or astrophysics, but I have a very broad understanding of the latest work in high energy physics, and the latest work on dark matter and dark energy phenomena, from the perspective of all of the relevant disciplines (although I admit that high energy physics theory is not my cup of tea and that I am less up to date in that area, seeing only papers that are cross-listed, discussed at the Physics Forums, or discussed at Physics Stack Exchange, for the most part).
Why is this approach to quantum gravity so great? Here are twenty reasons:
1. It explains "dark matter" phenomena and "dark energy" phenomena without introducing new particles or new forces.
2. It explains gravity (in principle, at least) with one less fundamental constant (the cosmological constant) than general relativity does, and two less than a relativistically generalized MOND theory like TeVeS.
3. It does not require extra dimensions.
4. It does not introduce Lorentz symmetry violations.
5. It is the only gravity theory of which I am aware that explains "dark energy" phenomena in a manner that does not violate conservation of mass-energy or require new non-Standard Model/non-General Relativity particles or attribute properties to aether (such as inherent curvature). It also explains the "cosmic coincidence" problem (i.e. that matter, dark matter and dark energy are present in quantities that are of roughly the same order of magnitude).
6. It is based upon interactions of the almost universally hypothesized particle, a graviton, with zero rest mass. This means, for example, that it is consistent with the evidence regarding the speed of gravity derived from the merger of a black hole and a neutron star observed with both gravitational wave detectors and telescopes.
7. It allows gravitational mass-energy to be localized to the same extent as any Standard Model interaction, and treats graviton-graviton interactions just like all other graviton-fundamental particle interactions.
8. It derives its phenomenological conclusions from first principles at the fundamental particle and interaction level in a very conventional manner that relies on no axioms that aren't entirely mainstream in quantum gravity research.
9. Because the first principles origins of the theory are known, it is possible to determine the correct form of equation to use in a way not possible with a purely phenomenologically derived description of what is observed.
10. Most investigators in the field agree that quantum gravity should be described by a non-Abelian quantum field theory with a self-interacting carrier boson, and its notable phenomenological conclusions flow directly from this aspect of this approach.
11. The phenomenological conclusions reached have close analogs in the best understood non-Abelian quantum field theory with a self-interacting carrier boson (i.e. QCD), in line with many prior investigators who have pursued the quantum gravity as "QCD squared" approach.
12. At least at a back of napkin calculation basis it is consistent with observed dark matter phenomena at the galaxy scale, at the galactic cluster scale, in the Bullet Cluster, and at the cosmology scale, although this has not been fleshed out and rigorously confirmed to the full extent that would be desirable.
13. The approach of doing calculations with the theory (which overcomes the common practical concern that naive quantum gravity using a massless spin-2 graviton isn't renormalizable), using a scalar graviton approximation, which is equivalent to a static equilibrium case in a tensor gravity theory, works. Also, it is possible to demonstrate that for the non-relativistic speed, astronomy scale processes it is being used to model, that this theoretical error introduced by using a scalar graviton (i.e. spin-0 graviton) approximation in lieu of a complete tensor graviton (i.e. spin-2 graviton) treatment is acceptably low. By analogy, in general relativity, in systems of these types, the theoretical error introduced by using a nearly Newtonian gravitational to general relativity introduces only very modest theoretical error.
14. It has predicted something (the relationship between the amount of apparent dark matter in elliptical galaxies and their shape) that was subsequently supported by the evidence.
15. It is mathematically consistent with the Standard Model and uses essentially the same mathematical framework as the Standard Model.
16. The respects in which it is contrary to conventional classical General Relativity, as commonly implemented by physicists today, give rise only to consequences that have not been tightly established by observational or experimental evidence.
17. It is reassuring that this has been done by a professional physicists with a sophisticated mathematical background and does not appeal to numerology or for example "Vedic physics."
18. The fact that it relies upon mathematical approaches that people with a QCD specialty, like Deur, are very familiar with, but are less familiar to people who specialize in general relativity or astronomy, helps to explain why no one else has come up with this in the last century, as does the fact that QCD and its associated mathematical conclusions themselves are only about 50 years old.
19. The fact that this approach comes to some conclusions (e.g. gravity can be localized, gravitational fields are an input, dark energy phenomena can arise without violating conservation of mass-energy) that are contrary to conventional, widely accepted maxims of general relativity, can help explain why no one else has come up with this in the last century. This factor and the previous one also explain why this approach has not received a lot of attention and support from other researcher in the field.
20. If this approach were validated, refined and widely adopted, this would pretty much be "the end of fundamental physics" as it this would leave no phenomena in the universe, prior to the first microsecond after the Big Bang, that was not fully described by the Standard Model plus this approach to quantum gravity. The main remaining inquiry would be to look for some deeper theory to describe why the many physically measured parameters of the Standard Model and quantum gravity have the values that they do. It would, for example, end the empirical motivation to look for new types of fundamental particles (other than the graviton) not found in the Standard Model.
What Unsolved Problems Of Physics Does It Solve?
Estimated distribution of dark matter and dark energy in the universe
- Quantum gravity: Can quantum mechanics and general relativity be realized as a fully consistent theory (perhaps as a quantum field theory)? Is spacetime fundamentally continuous or discrete? Would a consistent theory involve a force mediated by a hypothetical graviton, or be a product of a discrete structure of spacetime itself (as in loop quantum gravity)? Are there deviations from the predictions of general relativity at very small or very large scales or in other extreme circumstances that flow from a quantum gravity theory?
- Extra dimensions: Does nature have more than four spacetime dimensions? If so, what is their size? Are dimensions a fundamental property of the universe or an emergent result of other physical laws? Can we experimentally observe evidence of higher spatial dimensions?
- Galaxy rotation problem: Is dark matter responsible for differences in observed and theoretical speed of stars revolving around the centre of galaxies, or is it something else?
- Quantum chromodynamics: . . . What determines the key features of QCD, and what is their relation to the nature of gravity and spacetime?