# Horava Gravity

Can anybody explain in brief what the content of this new research program is?
- where does it come from?
- what are the main ideas and ingredients?
- what are the common aspects / main differences compared to other approaches?
- ...
- is there already some kind of review, e.g. an article, slides, a talk, ...?

It's interesting that this new approach attracts so many people in a very short time (4 month from the first paper in arxiv); there IS something and I would like to understand the main ideas w/o going through all these papers.

atyy
Last edited by a moderator:
Demystifier
Gold Member
Here are the basic ideas:
- Quantum variant of Einstein-Hilbert gravity is not renormalizable
- Non-renormalizability could be overcomed if the propagators had higher powers of k^2 in the denominator, because then loop integrals could become less divergenet or even finite
- Higher powers of k^2 correspond to an effective action with higher derivatives
- Due to Lorentz invariance the higher derivatives occur not only in space but also in time
- Higher derivatives in time imply that the theory has additional degrees of freedom - ghosts - that make troubles
- This leads to the Horava's idea - let us propose an action which has higher derivatives in space, but not in time - such a theory of gravity is renormalizable and ghost-free, but is not Lorentz invariant
- At large distances (at which higher-derivative terms in the action can be neglected) the theory reduces to the Einstein-Hilbert theory, which makes the theory consistent with observations

Now we have a NEW classical action for gravity the solutions of which can be studied even at the classical level, without actually quantizing it. This fact makes it relatively EASY to calculate various new stuff, which is one of the main reasons why so many papers appeared in a very short time. In addition to being easy, it is also INTERESTING, because it is related to a theory that at the quantum level is renormalizable.

Further advantages with respect to other theories:
Compared to string theory - much simpler and works in 3+1 dimensions
Compared to LQG - the classical limit is not a problem

Last edited:
Demystifier
Gold Member
My own contribution:
The absence of Lorentz invariance helps to solve the problem of quantum particles in classical gravitational backgrounds:
http://xxx.lanl.gov/abs/0904.3412

Haelfix
I agree with Demystifier that it appears to be an interesting theory precisely b/c you can calculate a lot of things in it. Those observables in turn might be related by universality to something more fundamentally sound, at least thats the hope.

Much like other modified gravity proposals that don't work for one reason or another, you can usually extract valuable insights from them.

The downside with this theory is the maximal amount of finetuning thats required (in general this is always the case when you break Lorentz invariance; upon RG flow operators that were normally under control can in principle recieve enormous corrections that can only be tamed by finetuning).

Demystifier
Gold Member
The downside with this theory is the maximal amount of finetuning thats required
Yes, that's the weakness of the theory, at least in its present formulation.

MTd2
Gold Member
Here are the basic ideas:
- Quantum variant of Einstein-Hilbert gravity is not renormalizable

But isn't there strong evidence that it is non perturbative renormalizable? I mean, this is one of recent discussions here, because it seems that Horava Gravity coincides with assymptotic safety in many aspects, like the continuous dimensions transition.

I think Marcus can say something better than I do.

Demystifier
Gold Member
But isn't there strong evidence that it is non perturbative renormalizable?
I'm not an expert, but I think it is questionable whether this evidence is "strong" enough.
It certainly isn't something generally accepted.

MTd2
Gold Member
I'm not an expert, but I think it is questionable whether this evidence is "strong" enough.

I know what you mean. It is questionable since until sometime ago there was no non-divergent term, from the perturbative expantion, included in the truncation. This is one of the things that Jacques Distler found fishy. But, recently, one such term was included, and shown that the method still yields a non perturbative renormalizable result, without significant changes to what was found without it. Well, as I said, Marcus can tell us more about this.

@Demystifier: Thanks a lot for the summary!

The major weakness seems to be that there's no guiding principle which terms are to be included. That's like f(R) gravity: you can include a lot of stuff and fit nearly everything after approriate adjusting and finetuning.

So the approach is nice but lacks a guidiung principle, e.g. a unique theory which produces Horava gravity in some appropriate limit.

Demystifier
Gold Member
@Demystifier: Thanks a lot for the summary!

The major weakness seems to be that there's no guiding principle which terms are to be included. That's like f(R) gravity: you can include a lot of stuff and fit nearly everything after approriate adjusting and finetuning.

So the approach is nice but lacks a guidiung principle, e.g. a unique theory which produces Horava gravity in some appropriate limit.
Well, Horava used the detailed balance principle to fix the action uniquely. But this principle does not seem to be necessary.

what do you mean by "... does not seem to be necessary"? Is there another way to fix the action?

Demystifier
Gold Member
what do you mean by "... does not seem to be necessary"? Is there another way to fix the action?
Actions that do not satisfy the detailed balance principle have also been proposed.
See e.g. arXiv:0904.1595

MTd2
Gold Member
I was checking the citations for that article that says that a scalar field does not decouple from the theory, and I found this:

http://arxiv.org/abs/0905.3423v1

It uses k-deformed algebra to fix that problem, which is kind of interesting given that it has been appearing whenever there is a fractal spacetime, a la Modesto, being consistent with assymptotic safety and LQG.

This another one also says that there is a way to get rid of the scalar:

http://arxiv.org/abs/0905.3821v1

It also cites the one above, but doesnt analyze much of it since it was posted on arxiv just 2 days after.

The funny thing it is that, although I understand little, it seems that with small corrections, that scalar can easily dealt with.