How Does Unimodular Gravity Influence Modern Quantum Gravity Theories?

[marcus]

Loll et al just put out a major review paper that relates Triangulations QG (CDT) to Horava Lifgarbagez, and also to UV-Fixed Point QG (Weinberg, Reuter, Percacci and others.)

http://arxiv.org/abs/0906.3947
Quantum gravity as sum over spacetimes
Jan Ambjorn, Jerzy Jurkiewicz, Renate Loll
67 pages, lectures given at the summer school "New Paths Towards Quantum Gravity", May 12-16 2008. To appear as part of a Springer Lecture Notes publication
(Submitted on 22 Jun 2009)
"A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known as "Causal Dynamical Triangulations" (CDT)."

What we seem to have here is the formation of a 4D gravity coalition sharing one or more common features such as: no extra dimensions, no drastic new degrees of freedom, modest means managing nevertheless to attain predictive UV finite theories of geometry/gravity.

We have seen how this coalition has tended to converge on some common results such as fracticality and reduced dimensionality at small scale, in some cases avoidance of cosmo singularity and replacement by bounce, hints of phenomenology accessible to astrophysical observation, etc. (GRB delay, CMB spectrum, polarization).

Now something new has come up. Recall that as we reported recently Smolin just posted a paper on Unimodular geometry/gravity and the Cosmo constant problem ( http://arxiv.org/abs/0904.4841 ) which mentioned the similarity with Loll's approach. Now Loll's group, in their new paper, cite Mikhail Shaposhnikov on Unimodular. That essentially means that Shapo's Unimod QG approach is part of coalition that is taking shape, and we should be aware of it and on the look-out.

Here are Shapo's papers:
http://arxiv.org/find/hep-th/1/au:+Shaposhnikov_M/0/1/0/all/0/1

Here is one of three papers of his that Loll cited:
http://arxiv.org/abs/0809.3395
Scale invariance, unimodular gravity and dark energy
Mikhail Shaposhnikov, Daniel Zenhausern
(Submitted on 19 Sep 2008)
"We demonstrate that the combination of the ideas of unimodular gravity, scale invariance, and the existence of an exactly massless dilaton leads to the evolution of the universe supported by present observations: inflation in the past, followed by the radiation and matter dominated stages and accelerated expansion at present. All mass scales in this type of theories come from one and the same source."

Thanks to John86 for flagging the Loll review paper! It looks like it will be extremely useful, and will be published in the Springer Lecture Notes series.

 

[marcus]

Curiously enough Smolin, in his paper http://arxiv.org/abs/0904.4841 pointed out the nice compatibility between Unimodular and Loll's Triangulations approach. Now this 67-page review by Loll's group bears the connection out.

BTW on the one hand Loll's CDT uses identical pentachor building blocks with a time-like foliation or layering.
And for its part, Unimodular geometry is like ordinary classic GR geometry except the diffeomorphisms have to be volume preserving, and has an inherent time-like index based on accumulated spacetime volume (you could almost call it a pentachor-count.) It's not hard to see the points of kinship.

This stuff from Loll and Shapo and Smolin may well step on cherished preconceptions, but I don't think it has to obstruct the emergence of Lorentz symmetry at an appropriate scale.

Anyway the main messages are keep an eye out for Mikhail Shaposhnikov and check the latest Loll et al review.

 

[atyy]

This stuff from Loll and Shapo and Smolin may well step on cherished preconceptions, but I don't think it has to obstruct the emergence of Lorentz symmetry at an appropriate scale.

Interesting they say that at the present level of numerical accuracy CDT is consistent with Asymptotic Safety or Horava-Lifgarbagez. I think AS is Lorentz invariant, but HL isn't.