Vacuum Zero Point Energy and its Statistical Correlations in dS Background

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 $⟨T⟩=-4⟨\rho ⟩$ for the vacuum stress energy tensor receives anomalous quantum correction which depends on the mass and the conformal coupling while the relation $⟨\rho ⟩=-⟨P⟩$ does hold. We calculate the density contrast associated to the vacuum zero point energy and show that $\delta \rho \sim ⟨\rho ⟩$ 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.

23 pages

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Cited by in corpus (1)

• Vacuum zero point energy of self-interacting quantum fields in dS background