Quantum thermodynamics in a static de Sitter space-time and initial state of the universe

TL;DR

This paper explores the quantum thermodynamics of a static de Sitter space-time using Relativistic Quantum Geometry, revealing discrete energy levels, temperature dependence on sub-states, and implications for the universe's primordial state.

Contribution

It introduces a novel quantum thermodynamical framework for de Sitter space-time, identifying discrete energy levels and linking them to primordial universe conditions.

Findings

Discrete energy levels for scalar fields in de Sitter space

Temperature and entropy depend on sub-state counts

Bekenstein-Hawking temperature recovered at infinite sub-states

Abstract

Using Relativistic Quantum Geometry we study back-reaction effects of space-time inside the causal horizon of a static de Sitter metric, in order to make a quantum thermodynamical description of space-time. We found a finite number of discrete energy levels for a scalar field from a polynomial condition of the confluent hypergeometric functions expanded around $r=0$. As in the previous work, we obtain that the uncertainty principle is valid for each energy level on sub-horizon scales of space-time. We found that temperature and entropy are dependent on the number of sub-states on each energy's level and the Bekenstein-Hawking temperature of each energy level is recovered when the number of sub-states of a given level tends to infinity. We propose that the primordial state of the universe could be described by a de Sitter metric with Planck energy $E_p=m_p\,c^2$, and a B-H temperature: $T_{BH}=\left(\frac{\hbar\,c}{2\pi\,l_p\,K_B}\right)$.