**15 March 2021***Space Science at Droptower SEMINAR TALK*

Location: **ZARM Bremen - Online seminar**

When: 15.3.2021, 17:00 CET - Online

**Speaker**: Jakub Bilski, (Zhejiang University of Technology, Hangzhou, People’s Republic of China)

**Title: **From canonical quantization of lattice gravity through its phase space reduction to anisotropic cosmology

Abstract: For the construction of a generally relativistic quantum field theory, background-independent quantum gravity is needed. By assuming the ADM decomposition of spacetime, it is possible to define the metric-independent discrete analog of a Fock space for quantum gravity on a lattice. This space, known as the spin network, is invariant under the SU(2) symmetry and the spatial diffeomorphisms transformations. It is the states space for loop quantum gravity.

I will describe an improved construction of the lattice regularization and cosmological reduction of the canonical formulation of loop quantum gravity. The application of this procedure to the Hamiltonian constraint provides its lattice analog, the domain of which has a natural structure of a sum of elementary cells. As a result, the related scalar constraint operator, which spectrum is independent of intertwiners, can be defined. The cosmological phase space reduction of lattice gravity requires a rigorous application of gauge-fixing conditions. The obtained Hamiltonian constraint is finite (without any cut-off introduction) and exact (with the holonomy expansion around the unit element of SU(2), known from QFT). It describes a simple structure of inhomogeneities and anisotropies. Consequently, the construction of the quantum evolution of the Universe in terms of transition amplitudes (instead of using perturbative approximations) appears to be possible.