Renormalizing the vacuum energy in cosmological spacetime: implications for the cosmological constant problem

Abstract

The renormalization of the vacuum energy in quantum field theory (QFT) is usually plagued with theoretical conundrums related not only with the renormalization procedure itself, but also with the fact that the final result leads usually to very large (finite) contributions incompatible with the measured value of $\Lambda$ in cosmology. Herein, we compute the zero-point energy (ZPE) for a nonminimally coupled (massive) scalar field in FLRW spacetime using the off-shell adiabatic renormalization technique employed in previous work. The general off-shell result yields a smooth function ${\rho }_{\mathrm{vac}}(H)$ made out of powers of the Hubble rate and/or of its time derivatives involving different (even) adiabatic orders $\sim H^N$ ($N=0,2,4,6,...)$, i.e. it leads, remarkably enough, to the running vacuum model (RVM) structure. We have verified the same result from the effective action formalism and used it to find the $\beta$-function of the running quantum vacuum. No undesired contributions $\sim m^4$ from particle masses appear and hence no fine-tuning of the parameters is needed in ${\rho }_{\mathrm{vac}}(H)$. Furthermore, we find that the higher power $\sim H^6$ could naturally drive RVM-inflation in the early universe. Our calculation also elucidates in detail the equation of state of the quantum vacuum: it proves to be not exactly $-1$ and is moderately dynamical. The form of ${\rho }_{\mathrm{vac}}(H)$ at low energies is also characteristic of the RVM and consists of an additive term (the so-called `cosmological constant') together with a small dynamical component $\sim \nu H^2$ ($|\nu |\ll 1$). Finally, we predict a slow ($\sim \ln H$) running of Newton's gravitational coupling $G(H)$. The physical outcome of our semiclassical QFT calculation is revealing: today's cosmic vacuum and the gravitational strength should be both mildly dynamical.

Typos corrected, references added

References in corpus (28)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Dynamics of dark energy
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Inflation scenario via the Standard Model Higgs boson and LHC
• Dark energy: a quantum fossil from the inflationary Universe?
• Dynamical vacuum energy in the expanding Universe confronted with observations: a dedicated study
• Cosmological Dark Energy: Prospects for a Dynamical Theory
• Cosmological Particle Production: A Review
• Hubble expansion and structure formation in the "running FLRW model" of the cosmic evolution
• The $\bar{\Lambda }CDM$ cosmology: from inflation to dark energy through running $\Lambda$
• The Cosmological Constant Problem and Running Vacuum in the Expanding Universe
• Running vacuum in quantum field theory in curved spacetime: renormalizing ${\rho }_{vac}$ without $\sim m^4$ terms
• Zero-point quantum fluctuations and dark energy
• Vacuum models with a linear and a quadratic term in H: structure formation and number counts analysis
• An Elementary Introduction to the JWKB Approximation
• Big Bang Nucleosynthesis constraints on higher-order modified gravities
• Dynamically avoiding fine-tuning the cosmological constant: the "Relaxed Universe"
• Fundamental constants and cosmic vacuum: the micro and macro connection
• Torsion in string-inspired cosmologies and the universe dark sector
• Vacuum fluctuations in a supersymmetric model in FRW spacetime
• Friedmann cosmology with decaying vacuum density in Brans-Dicke theory
• Do we Come from a Quantum Anomaly?
• Artificial Dynamical Effects in Quantum Field Theory
• Running gravitational couplings, decoupling, and curved spacetime renormalization
• The cosmological constant and Higgs mass with emergent gauge symmetries
• On Adiabatic Renormalization with a Physically Motivated Infrared Cut-Off

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• Current data are consistent with flat spatial hypersurfaces in the $\Lambda$CDM cosmological model but favor more lensing than the model predicts
• Alleviating $H_0$ Tension with New Gravitational Scalar Tensor Theories
• Anisotropic f(Q) gravity model with bulk viscosity
• Artificial Dynamical Effects in Quantum Field Theory
• Dynamical systems of cosmological models for different possibilities of $G$ and ${\rho }_{\Lambda }$
• Cosmological Constant and Vacuum Zero Point Energy in Black Hole Backgrounds
• Quadratic gravity potentials in de Sitter spacetime from Feynman diagrams