Loop quantum $f(R)$ theories

Understand

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.