Tomographic Representation of Minisuperspace Quantum Cosmology and Noether Symmetries

TL;DR

This paper develops a probability-based approach to quantum cosmology using tomographic representations, linking symmetries and observables to better understand classical evolution in minisuperspace models.

Contribution

It introduces a tomographic probability framework for minisuperspace quantum cosmology, incorporating Noether symmetries and applying it to Extended Theories of Gravity.

Findings

Tomographic distributions describe classical evolution of cosmological models.

Connection established between symmetries, tomograms, and cosmological parameters.

Examples from Extended Theories of Gravity demonstrate the approach.

Abstract

The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic probability distribution provides the classical evolution for the models and can be considered an approach to select "observable" universes. Some specific examples, derived from Extended Theories of Gravity, are worked out. We discuss also how to connect tomograms, symmetries and cosmological parameters.