Noether Symmetries and Quantum Cosmology in Extended Teleparallel Gravity

TL;DR

This paper uses Noether symmetries to identify minisuperspaces in extended teleparallel gravity, deriving quantum wave functions of the universe and classical trajectories that could describe observable cosmological evolutions.

Contribution

It introduces a novel application of Noether symmetry methods to quantum cosmology within extended teleparallel gravity, linking symmetries to quantum solutions and classical trajectories.

Findings

Derived minisuperspaces suitable for quantum cosmology

Obtained wave functions of the universe using ADM formalism

Identified classical trajectories interpretable as observable universes

Abstract

We apply the Noether Symmetry Approach to point-like teleparallel Lagrangians in view to derive minisuperspaces suitable for Quantum Cosmology. Adopting the Arnowitt-Deser-Misner formalism, we find out related Wave Functions of the Universe. Specifically, by means of appropriate changes of variables suggested by the existence of Noether symmetries, it is possible to obtain the cosmological Hamiltonians whose solutions are classical trajectories interpretable as observable universes.