Vacuum Zero Point Energy and its Statistical Correlations in dS Background

TL;DR

This paper investigates the quantum vacuum zero point energy in de Sitter space, revealing anomalous corrections, inhomogeneous distributions, and non-Gaussian features of the energy and pressure fluctuations.

Contribution

It provides a detailed calculation of the vacuum zero point energy and its statistical correlations in a de Sitter background, including quantum corrections and non-Gaussianity analysis.

Findings

Quantum correction modifies classical stress-energy relations.

Vacuum energy distribution is inhomogeneous and non-perturbative.

Zero point energy fluctuations are highly non-Gaussian.

Abstract

We study the vacuum zero point energy associated to a scalar field with an arbitrary mass and conformal coupling in a dS background. Employing dimensional regularization scheme, we calculate the regularized zero point energy density, pressure and the trace of the energy momentum tensor. It is shown that the classical relation $\langle T \rangle =-4 \langle \rho \rangle$ for the vacuum stress energy tensor receives anomalous quantum correction which depends on the mass and the conformal coupling while the relation $\langle \rho \rangle = - \langle P \rangle$ does hold. We calculate the density contrast associated to the vacuum zero point energy and show that $\delta \rho \sim \langle \rho \rangle$ indicating an inhomogeneous and non-perturbative distribution of the zero point energy. Finally, we calculate the skewness associated to the distribution of the zero point energy and pressure and show that they are highly non-Gaussian.