Energy stored on a cosmological horizon and its thermodynamic fluctuations in holographic equipartition law

TL;DR

This paper explores the energy and thermodynamic fluctuations on the cosmological horizon within a holographic framework, suggesting a connection to dark energy and the cosmological constant problem.

Contribution

It demonstrates that the energy on the Hubble horizon in a de Sitter universe aligns with observed cosmological constant scales and analyzes horizon energy fluctuations in a thermodynamic context.

Findings

Energy density on the horizon is constant and matches the order of the observed cosmological constant.

Thermodynamic energy fluctuations are universal and of the order of the Planck energy.

Relative fluctuations are extremely small, within the range relevant to the cosmological constant problem.

Abstract

Our Universe is expected to finally approach a de Sitter universe whose horizon is considered to be in thermal equilibrium. In the present article, both the energy stored on the horizon and its thermodynamic fluctuations are examined through the holographic equipartition law. First, it is confirmed that a flat Friedmann--Robertson--Walker universe approaches a de Sitter universe, using a cosmological model close to lambda cold dark matter ($\Lambda$CDM) models. Then, based on the holographic equipartition law, the energy density of the Hubble volume is calculated from the energy on the Hubble horizon of a de Sitter universe. The energy density for a de Sitter universe is constant and the order of the energy density is consistent with the order of that for the observed cosmological constant. Second, thermodynamic fluctuations of energy on the horizon are examined, assuming stable fluctuations around thermal equilibrium states. A standard formulation of the fluctuations for a canonical ensemble is applied to the Hubble horizon of a de Sitter universe. The thermodynamic fluctuations of the energy are found to be a universal constant corresponding to the Planck energy, regardless of the Hubble parameter. In contrast, the relative fluctuations of the energy can be characterized by the ratio of the one-degree-of-freedom energy to the Planck energy. At the present time, the order of the relative fluctuations should be within the range of a discrepancy derived from a discussion of the cosmological constant problem, namely a range approximately from $10^{-60}$ to $10^{-123}$. The present results may imply that the energy stored on the Hubble horizon is related to a kind of effective dark energy, whereas the energy that can be `maximally' stored on the horizon may behave as if it were a kind of effective vacuum-like energy in an extended holographic equipartition law.