For anyone not familiar with Bengtsson here are 34 papers in gr-qc, hep-th, and quant-ph going back to 1992(adsbygoogle = window.adsbygoogle || []).push({});

http://arxiv.org/find/grp_physics/1/au:+Bengtsson_I/0/1/0/all/0/1

He picked up fast on Krasnov's idea for (renormalizable) non-metric gravity.

http://arxiv.org/abs/gr-qc/0703114

Note on non-metric gravity

Ingemar Bengtsson

9 pages

"We discuss a class of alternative gravity theories that are specific to four dimensions, do not introduce new degrees of freedom, and come with a physical motivation. In particular we sketch their Hamiltonian formulation, and their relation to some earlier constructions."

This refers to two recent papers by Kirill Krasnov

http://arxiv.org/abs/hep-th/0611182

Renormalizable Non-Metric Quantum Gravity?

http://arxiv.org/abs/gr-qc/0703002

Non-Metric Gravity I: Field Equations

It's a new idea. Krasnov gave a seminar talk at Perimeter about it recently, available video in PIRSA, with Smolin asking him questions.

Here is Bengtsson's opening paragraph:

A class of alternative gravity theories were recently introduced, under the name of “non-metric gravity” [1].There are reasons to take this class seriously, in particular arguments were advanced why this class—which is defined by one free function of two variables—should be closed under renormalization [2]. Indeed the construction isinteresting already on the classical level, since it does not introduce any new degrees of freedom, as compared to GR (which is a member of the class); moreover the construction isintrinsically four dimensional(arguably a good thing), and is based on a clean split between conformal structure and conformal factor of the metric. In fact the split is so clean that the latter is largely lost track of, which brings us to some weak points of these models. The first of those is that the models describecomplex spacetimes, and it is not clear how to recover the Lorentzian sector. The second is that they appear to be quite difficult to couple to matter (but this may turn out to be a strong point in the end).

The purpose of this note is to clarify the relation between non-metric gravity and an earlier class of models with similar properties [3, 4]. The starting point is Plebánski’s action for vacuum general relativity...

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# Bengtsson picks up on Krasnov's non-metric gravity

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