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Loop quantum $f(R)$ theories
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abstract
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.
Forward citations
Cited by 2 Pith papers
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Consistency check on the fundamental and alternative flux operators in loop quantum gravity
A graphical consistency check between the fundamental and alternative flux operators in loop quantum gravity fixes the volume-operator constant κ_reg to 1/2.
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Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
Modified gravity theories supply viable mathematical frameworks for inflation, bounces, and dark energy eras that match observational data.
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