Improved (μ)over-bar-scheme effective dynamics of full loop quantum gravity

We propose a new derivation from full loop quantum gravity (LQG) to the loop quantum cosmology improved (mu) over bar -scheme effective dynamics, based on the reduced phase-space formulation of LQG and a proposal of an effective Hamiltonian/action in full LQG. A key step of our program is an improved regularization of full LQG Hamiltonian on a cubic lattice. The improved Hamiltonian uses a set of dressed holonomies h(Delta) (s) which depend on both the connection A and the length of the curve s. With the improved Hamiltonian, we propose a quantum effective action and derive a new set of effective equations of motion (EOMs) for full LQG. Then, we show that these new EOMs imply the (mu) over bar -scheme effective dynamics for both the homogeneous-isotropic and Bianchi-I cosmologies, and predict a bounce and Planckian critical density. As a byproduct, although the model is defined on a cubic lattice, we find that the improved effective Hamiltonian of cosmology is invariant under lattice refinement. The cosmological effective dynamics, predictions for the bounce, and critical density are results in the continuum limit.