nLab unimodular gravity

Idea

In theoretical physics, unimodular gravity refers to theories of gravity (general relativity) where the determinant of the metric tensor is constrained to unity.

This constraint restricts the diffeomorphism-invariance of these theories to volume-preserving diffeomorphisms.

References

General

The idea goes back to:

• Albert Einstein: Spielen Gravitationsfelder im Aufbau der materiellen Elementarteilchen eine wesentliche Rolle? Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) (1919) 349-356 [doi:10.1007/978-3-663-19510-8_10]

Early modern discussion:

• James L. Anderson, David Finkelstein: Cosmological Constant and Fundamental Length, Am. J. Phys. 39 (1971) 901–904 [doi:10.1119/1.1986321]

• William G. Unruh, Unimodular theory of canonical quantum gravity, Phys. Rev. D 40 (1989) 1048-1052 [doi:10.1103/PhysRevD.40.1048]

Review:

• Enrique Álvarez, Eduardo Velasco-Aja, A Primer on Unimodular Gravity, in Handbook of Quantum Gravity, Springer (2023) [arXiv:2301.07641]

For FQH excitations

On unimodular gravity as an effective field theory for the collective excitations of FQH systems:

• Andrey Gromov, Dam Thanh Son: Bimetric Theory of Fractional Quantum Hall States, Phys. Rev. X 7 041032 (2017) [arXiv:1705.06739, doi:10.1103/PhysRevX.7.041032]