Krasnov non-metric quantum gravity

In summary: The first effect, in particular, is of direct experimental interest and provides a probe of the strong field regime of general relativity."This third paper in the series is all about modifying gravity in interesting ways. One of the effects is a correction to Newton's law. It's interesting to think about what kind of experiments might be able to detect this.
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Jal called attention to Krasnov's most recent paper on non-metric QG.

here's a video of K.'s most recent Perimeter talk, about NMQG

you get to hear Lee Smolin and several others (Thiemann?, Freidel?) asking him questions.

NMQG is a dark horse (a "surprise candidate"). it wasn't expected. K. impresses me as a "loner"
maybe he is what Smolin calls a "valley crosser"

he has gone off the beaten path here. I think his new work is hard to evaluate or make predictions about, but could be important.
If someone else wants to try to evaluate, I would be very interested to hear what you think.

I printed Krasnov 16 November paper for myself when it came out, and likewise his most recent NMQG from a couple of days ago, and have been reading them on my own---but didn't call others' attention.
Thanks to Jal for calling attention to this interesting new work.
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Renormalizable Non-Metric Quantum Gravity?
Kirill Krasnov
5 pages

We argue that four-dimensional quantum gravity may be essentially renormalizable provided one relaxes the assumption of metricity of the theory. We work with Plebanski formulation of general relativity in which the metric (tetrad), the connection as well as the curvature are all independent variables and the usual relations among these quantities are only on-shell. One of the Euler-Lagrange equations of this theory guarantees its metricity. We show that quantum corrections generate a counterterm that destroys this metricity property, and that there are no other counterterms, at least at the one-loop level. There is a new coupling constant that controls the non-metric character of the theory. Its beta-function can be computed and is negative, which shows that the non-metricity becomes important in the infra red. The new IR-relevant term in the action is akin to a curvature dependent cosmological 'constant' and may provide a mechanism for naturally small 'dark energy'. "

The very long distance regime (infra red) is where the puzzles are these days----galactic rotation curves, accelerating expansion, generally speaking long-distance effects that have inspired people to invent dark energy and dark matter. It would be nice if part of the explanation had to do with something simple, like the failure of spacetime geometry to be given by a metric.
Non-Metric Gravity I: Field Equations
Kirill Krasnov
21 pages

"We describe and study a certain class of modified gravity theories. Our starting point is Plebanski formulation of gravity in terms of a triple of 2-forms, a connection A and a 'Lagrange multiplier' field Psi. The generalization we consider stems from presence in the action of an extra term proportional to a scalar function of Psi. As in the usual Plebanski general relativity (GR) case, the equations coming from variations with respect to Psi imply that a certain metric can be introduced. However, unlike in GR, the connection A no longer coincides with the self-dual part of the metric-compatible spin-connection. Field equations of the theory are shown to be relations between derivatives of the metric and components of field Psi, as well as its derivatives, the later being in contrast to the GR case. The equations are of second order in derivatives. An analog of the Bianchi identity is still present in the theory, as well as its contracted version tantamount to energy conservation equation. The arising modifications to the later are possibly of experimental significance."
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marcus said:
I printed Krasnov 16 November paper for myself when it came out, and likewise his most recent NMQG from a couple of days ago, and have been reading them on my own---but didn't call others' attention.


marcus said:
I would be very interested to hear what you think.

You first.
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The third paper in this series by Krasnov:
Non-Metric Gravity II: Spherically Symmetric Solution, Missing Mass and Redshifts of Quasars
Kirill Krasnov, Yuri Shtanov
37 pages, 2 figures

"We continue the study of the non-metric theory of gravity introduced in hep-th/0611182 and gr-qc/0703002 and obtain its general spherically symmetric vacuum solution. It respects the analog of the Birkhoff theorem, i.e., the vacuum spherically symmetric solution is necessarily static. As in general relativity, the spherically symmetric solution is seen to describe a black hole. The exterior geometry is essentially the same as in the Schwarzschild case, with power-law corrections to the Newtonian potential. The behavior inside the black-hole region is different from the Schwarzschild case in that the usual spacetime singularity gets replaced by a singular of a new type, where all basic fields of the theory remain finite but metric ceases to exist. The theory does not admit arbitrarily small black holes: for small objects, the curvature on the would-be horizon is so strong that non-metric modifications prevent the horizon from being formed. The theory allows for modifications of gravity of very interesting nature. We discuss three physical effects, namely, (i) correction to Newton's law in the neighborhood of the source, (ii) renormalization of effective gravitational and cosmological constants at large distances from the source, and (iii) additional redshift factor between spatial regions of different curvature. The first two effects can be responsible, respectively, for the observed anomaly in the acceleration of the Pioneer spacecraft and for the alleged missing mass in spiral galaxies and other astrophysical objects. The third effect can be used to propose a non-cosmological explanation of high redshifts of quasars."

Co-author Yuri Shtanov has 25 arxiv papers (mostly in BRANE COSMOLOGY) going back to 1994 when he was at Brown and also at the Kiev Bogolyubov Institute. I don't know about earlier non-arxiv papers.

Ingemar Bengtsson who is one of the board of directors of the new QGQG network of the ESF (Euro. Sci. Found.) has written a paper about this new approach of Krasnov (and now Shtanov). Krasnov is a professor of physics at Uni Nottingham IIRC, so a colleague of John Barrett, QGQG chairman.
This approach could turn out to take root in Europe or maybe also at Perimeter.

Interesting that Shtanov would depart from his usual Brane Cosmology pursuits and cross over and get interested in this more background independent (non-string) geometrical Quantum Gravity initiative of Krasnov.
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Short exerpt from pages 2 and 3 of the most recent non-metric gravity paper

"The nature of this modification of gravity is quite special and deserves a few words. In the numerous existing schemes of modified gravity, one usually deals with a metric theory and modifies the Hilbert–Einstein action by introducing extra degrees of freedom--either by increasing the number of derivatives (higher-derivative gravity), or by introducing extra fields (scalar-vector-tensor theories), or by considering extra dimensions (braneworlds).

Nothing of the listed takes place in our generalization: the theory remains four-dimensional, there are no extra fields, and the number of derivatives is not increased. Instead, the geometric structure of the theory is modified making it not quite “metric” in the sense described above..."

Krasnov: Read my lips: no extra fields. No extra dimensions. :biggrin:
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Krasnov has just posted a new paper on non-metric gravity. A journal (MPLA) asked him to write a review of this line of research. It is an impressive paper.
Non-metric gravity: A status report
Kirill Krasnov
13 pages, no figures, invited review for Modern Physics Letters A
(Submitted on 5 Nov 2007)

"We review the status of a certain (infinite) class of four-dimensional generally covariant theories propagating two degrees of freedom that are formulated without any direct mention of the metric. General relativity itself (in its Plebanski formulation) belongs to the class, so these theories are examples of modified gravity. We summarize the current understanding of the nature of the modification, of the renormalizability properties of these theories, of their coupling to matter fields, and describe some of their physical properties."

I went back to Krasnov's online video seminar talk. I'd encourage anyone to watch it.

He has a deeper mathematical understanding of the Plebanski formulation of gravity than any other I've heard.
dynamic Hodge dual operator----replacing the dynamic metric
Usually written * for "Hodge star". very basic concept in differential geometry.

deeper understanding of issues around renormalizability and non-renormalizability

Krasnov's investigations into Hodge star gravity (i.e. instead of metric d.o.f. gravity) seem to connect at some level with asymptotic safety.

I have to go out this evening----will get back to this later tonight or tomorrow.
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Just to remind. 2 new articles based on this approach:

Motion of a "small body" in non-metric gravity
Authors: Kirill Krasnov
(Submitted on 18 Dec 2008)

"Abstract: We describe "small bodies" in a non-metric gravity theory previously studied by this author. The main dynamical field of the theory is a certain triple of two-forms rather than the metric, with only the spacetime conformal structure, not metric, being canonically defined. The theory is obtained from general relativity (GR) in Plebanski formulation by adding to the action a certain potential. Importantly, the modification does not change the number of propagating degrees of freedom as compared to GR. We find that "small bodies" move along geodesics of a certain metric that is constructed with the help of a new potential function that appears in the matter sector. We then use the "small body" results to formulate a prescription for coupling the theory to general stress-energy tensor. In its final formulation the theory takes an entirely standard form, with matter propagating in a metric background and only the matter-gravity coupling and the gravitational dynamics being modified. This completes the construction of the theory and opens way to an analysis of its physical predictions."

Modified gravity without new degrees of freedom
Laurent Freidel
19 pages
(Submitted on 17 Dec 2008)
"We show that the new type of "non-metric" gravity theories introduced independently by Bengtsson and Krasnov can in fact be reexpressed explicitely as a metrical theory coupled to an auxiliary field. We unravel why such theories possesses only one propagating graviton by looking at the quadratic perturbation around a fixed solution. And we give a general construction principle with a new class of example of such modified gravity theories still possessing only two propagating degrees of freedom."

1. What is Krasnov non-metric quantum gravity?

Krasnov non-metric quantum gravity is a theoretical framework proposed by physicist Kirill Krasnov that aims to unify quantum mechanics and general relativity by describing gravity as a quantum field. It is based on the idea that space-time is made up of discrete building blocks rather than being continuous.

2. How does Krasnov non-metric quantum gravity differ from other theories of quantum gravity?

Krasnov non-metric quantum gravity differs from other theories, such as string theory and loop quantum gravity, in its approach to describing the underlying structure of space-time. It does not rely on the concept of a fixed metric or continuous space-time, but instead describes space-time as a discrete structure.

3. What is the current status of research on Krasnov non-metric quantum gravity?

Research on Krasnov non-metric quantum gravity is ongoing and there have been several developments in recent years. Some researchers have proposed new variations of the theory, while others are working on mathematical and computational tools to study its predictions. However, there is currently no experimental evidence to support the theory.

4. What are some potential applications of Krasnov non-metric quantum gravity?

If Krasnov non-metric quantum gravity is proven to be a valid theory, it could have significant implications for our understanding of the universe and could potentially lead to the development of new technologies. It could also help to resolve longstanding issues in cosmology and quantum physics, such as the nature of black holes and the origin of the universe.

5. What are some criticisms of Krasnov non-metric quantum gravity?

Some physicists have raised concerns about the lack of experimental evidence for Krasnov non-metric quantum gravity and the mathematical complexities of the theory. Additionally, some argue that it is too early to determine the validity of the theory until more research and testing is conducted. Some also question whether the theory can truly reconcile the fundamental principles of quantum mechanics and general relativity.

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