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

Vacuum Zero Point Energy and its Statistical Correlations in dS Background