http://arxiv.org/abs/2012.14242
Given the Loop-Quantum-Gravity (LQG) non-graph-changing Hamiltonian $\widehat{H[N]}$, the coherent state expectation value $\langle\widehat{H[N]}\rangle$ admits an semiclassical expansion in $\ell^2_{\rm p}$. In this paper, we compute explicitly the expansion of $\langle\widehat{H[N]}\rangle$ on the cubic graph to the linear order in $\ell^2_{\rm p}$, when the coherent state is peaked at the homogeneous and isotropic data of cosmology. In our computation, a powerful algorithm is developed to overcome the complexity in computing $\langle \widehat{H[N]} \rangle$. In particular, some key innovations in our algorithm substantially reduce the computational complexity in the Lorentzian part of $\langle\widehat{H[N]}\rangle$. In addition, some effects in cosmology from the quantum correction in $\langle\widehat{H[N]}\rangle$ are discussed at the end of this paper.
C. Zhang, S. Song and M. Han
Wed, 10 Feb 21
9/64
Comments: 29 pages, 2 figures, Theorem 4.4 is revised