Classification of primary constraints of quadratic non-metricity theories of gravity. (English) Zbl 1460.83065
Summary: We perform the ADM decomposition of a five-parameter family of quadratic non-metricity theories and study their conjugate momenta. After systematically identifying all possible conditions which can be imposed on the parameters such that different sets of primary constraints arise, we find that the five-parametric theory space can be compartmentalized into nine different sectors, based on the presence or absence of primary constraints. This classification allows to dismiss certain classes of theories as unphysical and invites further investigations into the remaining sectors, which may contain phenomenologically interesting modifications of General Relativity.
MSC:
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C40 | Gravitational energy and conservation laws; groups of motions |
| 83C45 | Quantization of the gravitational field |
| 53Z05 | Applications of differential geometry to physics |
Software:
xActReferences:
| [1] | Aldrovandi, R.; Pereira, JG, Teleparallel gravity (2013), Germany: Springer, Germany · Zbl 1259.83002 · doi:10.1007/978-94-007-5143-9 |
| [2] | Y.-F. Cai, S. Capozziello, M. De Laurentis and E. N. Saridakis, f (T) teleparallel gravity and cosmology, Rept. Prog. Phys.79 (2016) 106901 [arXiv:1511.07586] [INSPIRE]. |
| [3] | Krssak, M.; van den Hoogen, RJ; Pereira, JG; Böhmer, CG; Coley, AA, Teleparallel theories of gravity: illuminating a fully invariant approach, Class. Quant. Grav., 36 (2019) · Zbl 1478.83205 · doi:10.1088/1361-6382/ab2e1f |
| [4] | Beltrán Jiménez, J.; Heisenberg, L.; Koivisto, TS, Teleparallel Palatini theories, JCAP, 08, 039 (2018) · Zbl 1536.83106 · doi:10.1088/1475-7516/2018/08/039 |
| [5] | Beltrán Jiménez, J.; Heisenberg, L.; Koivisto, T., Coincident general relativity, Phys. Rev. D, 98 (2018) · doi:10.1103/PhysRevD.98.044048 |
| [6] | Beltrán Jiménez, J.; Heisenberg, L.; Koivisto, TS; Pekar, S., Cosmology in f (Q) geometry, Phys. Rev. D, 101, 103507 (2020) · doi:10.1103/PhysRevD.101.103507 |
| [7] | P. A. M. Dirac, Generalized Hamiltonian dynamics, Canadian J. Math.2 (1950) 129. · Zbl 0036.14104 |
| [8] | Anderson, JL; Bergmann, PG, Constraints in covariant field theories, Phys. Rev., 83, 1018 (1951) · Zbl 0045.45505 · doi:10.1103/PhysRev.83.1018 |
| [9] | Dirac, PAM, Lectures on quantum mechanics (1964), Boston, U.S.A: Dover Publications, Boston, U.S.A |
| [10] | J. M. Martín-García, xAct: efficient tensor computer algebra for the Wolfram Language, http://www.xact.es/. |
| [11] | F. D’Ambrosio, M. Garg, L. Heisenberg and S. Zentarra, ADM formulation and Hamiltonian analysis of coincident general relativity, arXiv:2007.03261 [INSPIRE]. |
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