Loop quantum $f(R)$ theories

Details Loop quantum $f(R)$ theories Loop quantum $f(R)$ theories

2011-07-25

arxiv.org/abs/1107.4921v2

Phys. Rev. D 84 (2011), 064040

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages; published version in PRD

Scientific paper

As modified gravity theories, the 4-dimensional metric $f(R)$ theories are cast into connection dynamical formalism with real $su(2)$-connections as configuration variables. This formalism enables us to extend the non-perturbative loop quantization scheme of general relativity to any metric $f(R)$ theories. The quantum kinematical framework of $f(R)$ gravity is rigorously constructed, where the quantum dynamics can be launched. Both Hamiltonian constraint operator and master constraint operator for $f(R)$ theories are well defined. Our results show that the non-perturbative quantization procedure of loop quantum gravity are valid not only for general relativity but also for a rather general class of 4-dimensional metric theories of gravity.

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