- #1

marcus

Science Advisor

Gold Member

Dearly Missed

- 24,757

- 788

Interest is gathering around unimodular General Relativity, so we should get some reference links together to facilitate following the research excursion into that area.

Einstein came up with unimodular GR around 1919, shortly after he proposed ordinary GR.

Here are some recent (and not-so-recent) papers on it:

http://arXiv.org/abs/hep-th/0501146

http://arXiv.org/cits/hep-th/0501146

Enrique Alvarez

http://arXiv.org/abs/hep-th/0702184

http://arXiv.org/cits/hep-th/0702184

Enrique Álvarez, Antón F. Faedo

23 pages, Phys.Rev.D76:064013,2007

"Some models are presented in which the strength of the gravitational coupling of the potential energy relative to the same coupling for the kinetic energy is, in a precise sense, adjustable. The gauge symmetry of these models consists of those coordinate changes with unit jacobian."

http://arxiv.org/abs/0801.4477

Hossein Farajollahi

Gen.Rel.Grav.37:383-390,2005

"A cosmological time variable is emerged from the hamiltonian formulation of unimodular theory of gravity to measure the evolution of dynamical observables in the theory. A set of constants of motion has been identified for the theory on the null hypersurfaces that its evolution is with respect to the volume clock introduced by the cosmological time variable."

http://arXiv.org/abs/0809.1371

http://arXiv.org/cits/0809.1371

Bartomeu Fiol, Jaume Garriga

17 pages

Some earlier papers:

http://arxiv.org/abs/hep-th/9911102

Y. Jack Ng, H. van Dam (University of North Carolina)

Int.J.Mod.Phys. D10 (2001) 49-56

"Recent astrophysical observations seem to indicate that the cosmological constant is small but nonzero and positive. The old cosmological constant problem asks why it is so small; we must now ask, in addition, why it is nonzero (and is in the range found by recent observations), and why it is positive. In this essay, we try to kill these three metaphorical birds with one stone. That stone is the unimodular theory of gravity, which is the ordinary theory of gravity, except for the way the cosmological constant arises in the theory. We argue that the cosmological constant becomes dynamical, and eventually, in terms of the cosmic scale factor R(t), it takes the form [tex]\Lambda(t) = \Lambda(t_0)(R(t_0)/R(t))^2[/tex], but not before the epoch corresponding to the redshift parameter [tex]z \sim 1[/tex].

W. G. Unruh, ”

D 40, 1048 (1989);

M. Henneaux and C. Teitelboim, “

The most recent paper on unimod GR is this one:

http://arxiv.org/abs/0904.4841

Lee Smolin

22 pages

(Submitted on 30 Apr 2009)

"A quantization of unimodular gravity is described, which results in a quantum effective action which is also unimodular, ie a function of a metric with fixed determinant. A consequence is that contributions to the energy momentum tensor of the form of the metric times a spacetime constant, whether classical or quantum, are not sources of curvature in the equations of motion derived from the quantum effective action. This solves the first cosmological constant problem, which is suppressing the enormous contributions to the cosmological constant coming from quantum corrections. We discuss several forms of uniodular gravity and put two of them, including one proposed by Henneaux and Teitelboim, in constrained Hamiltonian form. The path integral is constructed from the latter. Furthermore, the second cosmological constant problem, which is why the measured value is so small, is also addressed by this theory. We argue that a mechanism first proposed by Ng and van Dam for suppressing the cosmological constant by quantum effects obtains at the semiclassical level."

For another approach to the cosmo constant problem, that doesn't use unimodular, there's a recent paper by Afshordi

http://arxiv.org/abs/0807.2639

Einstein came up with unimodular GR around 1919, shortly after he proposed ordinary GR.

Here are some recent (and not-so-recent) papers on it:

http://arXiv.org/abs/hep-th/0501146

http://arXiv.org/cits/hep-th/0501146

**Can one tell Einstein's unimodular theory from Einstein's general relativity?**Enrique Alvarez

http://arXiv.org/abs/hep-th/0702184

http://arXiv.org/cits/hep-th/0702184

**Unimodular cosmology and the weight of energy**Enrique Álvarez, Antón F. Faedo

23 pages, Phys.Rev.D76:064013,2007

"Some models are presented in which the strength of the gravitational coupling of the potential energy relative to the same coupling for the kinetic energy is, in a precise sense, adjustable. The gauge symmetry of these models consists of those coordinate changes with unit jacobian."

http://arxiv.org/abs/0801.4477

**Time and Observables in Unimodular General Relativity**Hossein Farajollahi

Gen.Rel.Grav.37:383-390,2005

"A cosmological time variable is emerged from the hamiltonian formulation of unimodular theory of gravity to measure the evolution of dynamical observables in the theory. A set of constants of motion has been identified for the theory on the null hypersurfaces that its evolution is with respect to the volume clock introduced by the cosmological time variable."

http://arXiv.org/abs/0809.1371

http://arXiv.org/cits/0809.1371

**Troubles for unimodular gravity**Bartomeu Fiol, Jaume Garriga

17 pages

Some earlier papers:

http://arxiv.org/abs/hep-th/9911102

**A small but nonzero cosmological constant**Y. Jack Ng, H. van Dam (University of North Carolina)

Int.J.Mod.Phys. D10 (2001) 49-56

"Recent astrophysical observations seem to indicate that the cosmological constant is small but nonzero and positive. The old cosmological constant problem asks why it is so small; we must now ask, in addition, why it is nonzero (and is in the range found by recent observations), and why it is positive. In this essay, we try to kill these three metaphorical birds with one stone. That stone is the unimodular theory of gravity, which is the ordinary theory of gravity, except for the way the cosmological constant arises in the theory. We argue that the cosmological constant becomes dynamical, and eventually, in terms of the cosmic scale factor R(t), it takes the form [tex]\Lambda(t) = \Lambda(t_0)(R(t_0)/R(t))^2[/tex], but not before the epoch corresponding to the redshift parameter [tex]z \sim 1[/tex].

W. G. Unruh, ”

**A Unimodular theory of canonical quantum gravity**,” Phys. Rev.D 40, 1048 (1989);

M. Henneaux and C. Teitelboim, “

**The cosmological constant and general covariance**,” Phys. Lett. B 222, 195 (1989).The most recent paper on unimod GR is this one:

http://arxiv.org/abs/0904.4841

**The quantization of unimodular gravity and the cosmological constant problem**Lee Smolin

22 pages

(Submitted on 30 Apr 2009)

"A quantization of unimodular gravity is described, which results in a quantum effective action which is also unimodular, ie a function of a metric with fixed determinant. A consequence is that contributions to the energy momentum tensor of the form of the metric times a spacetime constant, whether classical or quantum, are not sources of curvature in the equations of motion derived from the quantum effective action. This solves the first cosmological constant problem, which is suppressing the enormous contributions to the cosmological constant coming from quantum corrections. We discuss several forms of uniodular gravity and put two of them, including one proposed by Henneaux and Teitelboim, in constrained Hamiltonian form. The path integral is constructed from the latter. Furthermore, the second cosmological constant problem, which is why the measured value is so small, is also addressed by this theory. We argue that a mechanism first proposed by Ng and van Dam for suppressing the cosmological constant by quantum effects obtains at the semiclassical level."

For another approach to the cosmo constant problem, that doesn't use unimodular, there's a recent paper by Afshordi

http://arxiv.org/abs/0807.2639

Last edited: