Local spinfoam expansion in loop quantum cosmology

TL;DR

This paper develops a local spinfoam expansion for vacuum Bianchi I models in loop quantum cosmology, removing the need for a matter clock and achieving a local amplitude, advancing the understanding of quantum cosmological dynamics.

Contribution

It introduces a method to obtain a local spinfoam expansion for vacuum Bianchi I models without using a matter clock, improving the formalism's applicability.

Findings

Successfully constructed a local spinfoam amplitude for vacuum Bianchi I.

Demonstrated the removal of matter clock dependence in the spinfoam formalism.

Provided a new regulator approach to achieve locality in the amplitude.

Abstract

The quantum dynamics of the flat Friedmann-Lemaitre-Robertson-Walker and Bianchi I models defined by loop quantum cosmology have recently been translated into a spinfoam-like formalism. The construction is facilitated by the presence of a massless scalar field which is used as an internal clock. The implicit integration over the matter variable leads to a nonlocal spinfoam amplitude. In this paper we consider a vacuum Bianchi I universe and show that by choosing an appropriate regulator a spinfoam expansion can be obtained without selecting a clock variable and that the resulting spinfoam amplitude is local.