Speaker
Description
We address the problem of defining a proper cosmological sector within Loop Quantum Gravity. Using a symmetry-reduction approach, we characterize the classical cosmological phase space with tools from differential topology, drawing inspiration from Yang-Mills theories and avoiding the usual minisuperspace reduction. Specifically, we propose a symmetry-reduction method based entirely on geometric considerations, which preserves local gauge symmetries. Consequently, our quantization scheme mirrors the LQG framework, allowing spin-network states to naturally emerge with properties analogous to the standard cosmological states.
In this talk, after a brief review of the necessary mathematical formalism, we discuss the imposition of symmetries at the classical level, focusing on the formal definition of homogeneity for the Ashtekar variables. We observe that, under our mathematical interpretation of homogeneity, the SU(2) gauge symmetry of the theory is preserved. The resulting system possesses a set of constraints analogous to those in LQG, enabling quantization in terms of spin networks. Furthermore, we demonstrate that these spin networks exhibit a notion of homogeneity, where the homogeneous spin-network states depend on point holonomies in a manner similar to the usual states in Loop Quantum Cosmology.
Additionally, our ongoing analysis of the moduli space of symmetry-reduced connections reveals favorable topological properties, suggesting that it is possible to define an Ashtekar-Lewandowski measure on this space without resorting to the construction of the set of generalized connections.
As a result, the cosmological states we construct share significant properties with both the LQC and LQG frameworks. This provides a simplified yet physically meaningful setting to implement and test quantum dynamics approaches proposed within LQG.
