Losing the trace to find dynamical Newton or Planck constants

0554630 - FZÚ 2022 RIV GB eng J - Journal Article
Jiroušek, Pavel - Shimada, K. - Vikman, Alexander - Yamaguchi, M.
Losing the trace to find dynamical Newton or Planck constants.
Journal of Cosmology and Astroparticle Physics. Roč. 4, Apr. (2021), č. článku 028. ISSN 1475-7516. E-ISSN 1475-7516
R&D Projects: GA ČR(CZ) GA20-28525S; GA MŠMT EF15_003/0000437
Grant - others:OP VVV - CoGraDS(XE) CZ.02.1.01/0.0/0.0/15_003/0000437
Institutional support: RVO:68378271
Keywords : modified gravity * gravity * quantum cosmology
OECD category: Particles and field physics
Impact factor: 7.280, year: 2021
Method of publishing: Limited access
https://doi.org/10.1088/1475-7516/2021/04/028

We show that promoting the trace part of the Einstein equations to a trivial identity results in the Newton constant being an integration constant. Thus, in this formulation the Newton constant is a global dynamical degree of freedom which is also a subject to quantization and quantum fluctuations. This is similar to what happens to the cosmological constant in the unimodular gravity where the trace part of the Einstein equations is lost in a different way. We introduce a constrained variational formulation of these modified Einstein equations. Then, drawing on analogies with the Henneaux-Teitelboim action for unimodular gravity, we construct different general-covariant actions resulting in these dynamics. The inverse of dynamical Newton constant is canonically conjugated to the Ricci scalar integrated over spacetime. Surprisingly, instead of the dynamical Newton constant one can formulate an equivalent theory with a dynamical Planck constant.
Permanent Link: http://hdl.handle.net/11104/0329335