Tomographic entropy and cosmology

TL;DR

This paper reviews the application of quantum tomographic methods and entropy concepts to cosmology and quantum gravity, exploring inequalities and bounds for the universe's quantum state.

Contribution

It introduces the notion of tomographic entropy in cosmology and derives inequalities that serve as bounds for the universe's quantum state.

Findings

Derived inequalities for tomographic probability distributions

Clarified the lower bound interpretation of tomographic entropy

Applied quantum tomography to minisuperspace models in cosmology

Abstract

The probability representation of quantum mechanics including propagators and tomograms of quantum states of the universe and its application to quantum gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator, free pointlike particle and repulsive oscillator are considered. The notion of tomographic entropy and its properties are used to find some inequalities for the tomographic probability determining the quantum state of the universe. The sense of the inequality as a lower bound for the entropy is clarified.