Mannheim's Conformal Gravity: Revisited
After my recent post, yesterday we were lucky to have Mannheim here at MIT. He is currently collaborating with Alan Guth on brane gravity models. We went thorough my blog entry. So I should summarize it before forgetting.
First of all he is not working in the field for thirty year but about fifteen now. He did start to study conformal gravity just for its mathematical beauty but in the end it turned out to be a solution for dark energy and dark matter. (I wonder if there are solutions for dark galaxies.) He initially named it as Weyl gravity but changed the name quickly to prevent confusions with Weyl geometry.
Variation with respect to conformal scaling field does not make any sense because it is not a new degree of freedom. Actually degrees of freedom in the theory are not different than GR.
He does not accept the von Neumann criticism because galaxy curves fit with just two universal constants instead of different dark and baryonic matter ratios for different galaxies in the standard theory. Interesting thing is these parameters as well as G itself is effective in this theory. You have to match interior and exterior of the source to find the "constant". For example you need the details of the QCD energy momentum tensor distribution inside the proton. Here comes the basic motivation that struck him many years ago. If QFT teaches us that inertial mass is dynamical then gravitational mass must be dynamical. This theory satisfies him in this respect. But I need to think more. His mass generation mechanism is similar (or exactly the same?) to Higgs.
Regarding to cosmology he has a significant prediction. There should not be a deceleration period in the universe history. Universe was always accelerating! I reminded him the current claims about the evidence for deceleration. He said he is well aware of them and they are not precise enough yet. He claimed that the data fits both possibilities still in equal amount of certainty. Two-sigma contours cover his range also. He also told me that his cosmological equations are not fourth order contrary to my first understanding.
He did not get important criticism related to the fundamental principles after many talks across the country for many years. But he accepts that the theory is not completely studied needs further work. He is the only man in the field. He finds it amazing that a theory which is so beautiful can predict dark matter and dark energy observations even though it is not designed to be.
He believes that the community is not ready for a theory that strikes had on GR and might be right. Cosmology hopefully will give better tests soon.
First of all he is not working in the field for thirty year but about fifteen now. He did start to study conformal gravity just for its mathematical beauty but in the end it turned out to be a solution for dark energy and dark matter. (I wonder if there are solutions for dark galaxies.) He initially named it as Weyl gravity but changed the name quickly to prevent confusions with Weyl geometry.
Variation with respect to conformal scaling field does not make any sense because it is not a new degree of freedom. Actually degrees of freedom in the theory are not different than GR.
He does not accept the von Neumann criticism because galaxy curves fit with just two universal constants instead of different dark and baryonic matter ratios for different galaxies in the standard theory. Interesting thing is these parameters as well as G itself is effective in this theory. You have to match interior and exterior of the source to find the "constant". For example you need the details of the QCD energy momentum tensor distribution inside the proton. Here comes the basic motivation that struck him many years ago. If QFT teaches us that inertial mass is dynamical then gravitational mass must be dynamical. This theory satisfies him in this respect. But I need to think more. His mass generation mechanism is similar (or exactly the same?) to Higgs.
Regarding to cosmology he has a significant prediction. There should not be a deceleration period in the universe history. Universe was always accelerating! I reminded him the current claims about the evidence for deceleration. He said he is well aware of them and they are not precise enough yet. He claimed that the data fits both possibilities still in equal amount of certainty. Two-sigma contours cover his range also. He also told me that his cosmological equations are not fourth order contrary to my first understanding.
He did not get important criticism related to the fundamental principles after many talks across the country for many years. But he accepts that the theory is not completely studied needs further work. He is the only man in the field. He finds it amazing that a theory which is so beautiful can predict dark matter and dark energy observations even though it is not designed to be.
He believes that the community is not ready for a theory that strikes had on GR and might be right. Cosmology hopefully will give better tests soon.
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