Zero Point Energy: Securitizing its Anomalies and Statistics

• Haidar Sheikhahmadi (School of Astronomy, IPM)

In this study, we investigate the properties of vacuum zero-point energy associated with a scalar field featuring arbitrary mass and conformal coupling within a de Sitter background. By employing a dimensional regularization scheme, we derive expressions for the regularized zero-point energy density, pressure, and trace of the energy-momentum tensor. Our findings reveal that the classical relation ⟨T⟩=−4⟨ρ⟩, which holds for the vacuum stress-energy tensor, experiences anomalous quantum corrections dependent on the mass and conformal coupling. However, we confirm that the relation ⟨ρ⟩=−⟨P⟩ remains valid. Furthermore, we delve into the density contrast associated with the vacuum zero-point energy, demonstrating that δρ∼⟨ρ⟩ signifies an inhomogeneous and non-perturbative distribution of the zero-point energy. Our investigation extends to calculating the skewness associated with the distribution of the zero-point energy and pressure. Intriguingly, we establish that these distributions exhibit highly non-Gaussian behaviour, highlighting the nontrivial nature of quantum effects in the system.