Entropy of Quantum Fields in de Sitter Space-time

TL;DR

This paper investigates the quantum states and entropy of quantum fields in de Sitter space-time using ambient space formalism, revealing a finite, observer-invariant entropy dependent on the Hubble constant and group Casimir eigenvalues.

Contribution

It introduces a novel approach to quantize fields in de Sitter space using a compact homogeneous space, resulting in a finite quantum state count and entropy calculation.

Findings

Number of quantum states is finite despite infinite-dimensional Hilbert space.

Quantum entropy is finite and invariant across inertial observers.

Quantum states depend on de Sitter topology and group representations.

Abstract

The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism. In this formalism, the quantum states are only depended $(1)$ on the topological character of the de Sitter space-time, {\it i.e.} $\R \times S^3$, and $(2)$ on the homogeneous spaces which are used for construction of the unitary irreducible representation of de Sitter group. A compact homogeneous space is chosen in this paper. The unique feature of this homogeneous space is that its total number of quantum states, ${\cal N}$, is finite although the Hilbert space has infinite dimensions. It is shown that ${\cal N}$ is a continuous function of the Hubble constant $H$ and the eigenvalue of the Casimir operators of de Sitter group. The entropy of the quantum fields on this Hilbert space have been calculated which is finite and invariant for all inertial observers on the de Sitter hyperboloid.