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arXiv · 2307.00977

Vacuum Zero Point Energy and its Statistical Correlations in dS Background

Hassan Firouzjahi·Haidar Sheikhahmadi
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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.

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Hassan Firouzjahi, Haidar Sheikhahmadi. 2023-07-03. Vacuum Zero Point Energy and its Statistical Correlations in dS Background. https://doi.org/10.1103/physrevd.108.065002

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