Cosmological Constant Problem and Renormalized Vacuum Energy Density in Curved Background

Abstract

The current vacuum energy density observed as dark energy ${\rho }_{\mathrm{dark}}\simeq 2.5\times 10^{-47}\mathrm{Ge}{\mathrm{V}}^4$ is unacceptably small compared with any other scales. Therefore, we encounter serious fine-tuning problem and theoretical difficulty to derive the dark energy. However, the theoretically attractive scenario has been proposed and discussed in literature: In terms of the renormalization-group (RG) running of the cosmological constant, the vacuum energy density can be expressed as ${\rho }_{\mathrm{vacuum}}\simeq m^2{H}^2$ where $m$ is the mass of the scalar field and rather dynamical in curved spacetime. However, there has been no rigorous proof to derive this expression and there are some criticisms about the physical interpretation of the RG running cosmological constant. In the present paper, we revisit the RG running effects of the cosmological constant and investigate the renormalized vacuum energy density in curved spacetime. We demonstrate that the vacuum energy density described by ${\rho }_{\mathrm{vacuum}}\simeq m^2{H}^2$ appears as quantum effects of the curved background rather than the running effects of cosmological constant. Comparing to cosmological observational data, we obtain an upper bound on the mass of the scalar fields to be smaller than the Planck mass, $m\lesssim M_{\mathrm{Pl}}$.

32 pages, references added, version accepted for publication in JCAP

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• Running vacuum in QFT in FLRW spacetime: The dynamics of ${\rho }_{\mathrm{vac}}(H)$ from the quantized matter fields
• Electroweak Vacuum Instability and Renormalized Vacuum Field Fluctuations in Friedmann-Lemaitre-Robertson-Walker Background
• Instability of De Sitter Spacetime induced by Quantum Conformal Anomaly
• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• Cosmic eggs to relax the cosmological constant
• Beta Function Quintessence Cosmological Parameters and Fundamental Constants I: Power and Inverse Power Law Dark Energy Potentials
• Running vacuum and H^4-inflation
• On the Field Theoretical Description of an Alternative Model to Generalized Chaplygin Gas and its Thermodynamic Behaviour
• Vacuum quantum effects on Lie groups with bi-invariant metrics