Question

What sorts of problems does asymptotically safe gravity face as a potential quantum gravity solution?

Answer 1

This approach might unify all particles and interactions and solve the quantum gravity problem. It is notably hard to test and one might ...

Answer 2

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In a way, asymptotically safe gravity is a huge disappointment. In quantum field theory, one needs to know all of the interactions between all of your fields in order to make predictions, but it happens that in the low-energy limit, many interactions become irrelevant and we only need to know the low-energy theory - in our case, the Standard Model coupled to non-renormalizable gravitons. If we do "fix" pure gravity with asymptotic safety, we know how pure gravity acts to all energies, but since every single form of energy/matter in our universe couples to gravity, we actually know very little about the high energy physics unless we simultaneously solve everything else in physics at the same time.

Extremely high-energy gravity will create extremely high-energy particles of every type whose interactions will then be important. So we'll need to know the interactions of everything up to the Planck scale if we actually want to know what's going on.one could still look at certain predictions of pure gravity like black holes and learn very interesting things, and probably solve some important problems.

But you couldn't make any quantitativeprediction in our universe at high energies without knowing everything in particle physics all the way to the Planck scale.String theory gets around this because it unifies particle physics with gravity at the outset. You can't have gravity without other particles, and their interactions are massively constrained. As far as I know, loop quantum gravity DOES suffer the same issue as asymptotic safety, but I'm open to corrections on this.