Towards the Understanding of Quantum Cosmology from Loop Quantum Gravity*

Loop quantum cosmology (LQC) provides an elegant resolution of the big bang singularity by a quantum bounce in the deep Planck era. Now an important issue that has remained open is its connection with loop quantum gravity (LQG). 

In this talk, I shall first give a brief review on various different approaches proposed so far, and then present our recent results of the cosmological dynamics resulting from an effective Hamiltonian, lately derived in LQG using Thiemann's regularization. Although the resulted  quantum difference equation is  of the fourth-order,  a non-singular bounce occurs generically. The corresponding dynamics can be described by either the Hamilton's or the Friedmann-Raychaudhuri equations, but the map between the two descriptions is not one-to-one. A careful analysis resolves the tension on symmetric versus asymmetric bounce in this model, showing that the bounce must be asymmetric and symmetric bounce is physically inconsistent, in contrast to the standard LQC. In addition, the current observations only allow a scenario where the pre-bounce branch is asymptotically de Sitter and the post-bounce branch yields the classical general relativity.