Running vacuum in QFT in FLRW spacetime: The dynamics of ${\rho }_{\mathrm{vac}}(H)$ from the quantized matter fields

Abstract

Phenomenological work in the last few years has provided significant support to the idea that the vacuum energy density (VED) is a running quantity with the cosmological evolution and that this running helps to alleviate the cosmological tensions afflicting the $\Lambda$CDM. On the theoretical side, recent devoted studies have shown that the properly renormalized ${\rho }_{\mathrm{vac}}$ in QFT in FLRW spacetime adopts the "running vacuum model" (RVM) form. While in three previous studies by two of us (CMP and JSP) such computations focused solely on scalar fields non-minimally coupled to gravity, in the present work we compute the spin-$1/2$ fermionic contributions and combine them both. The calculation is performed using a new version of the adiabatic renormalization procedure based on subtracting the UV divergences at an off-shell renormalization point $M$. The quantum scaling of ${\rho }_{\mathrm{vac}}$ with $M$ turns into cosmic evolution with the Hubble rate, $H$. As a result the "cosmological constant" $\Lambda$ appears in our framework as the nearly sustained value of $8\pi G(H){\rho }_{\mathrm{vac}}(H)$ around (any) given epoch $H$, where $G(H)$ is the gravitational coupling, which is also running, although very mildly (logarithmically). We find that the VED evolution at present reads $\delta {\rho }_{\mathrm{vac}}(H)\sim {\nu }_{\mathrm{eff}}{m}_{\mathrm{Pl}}^2\left(H^2-H_0^2\right)(|{\nu }_{\mathrm{eff}}|\ll 1)$. The coefficient ${\nu }_{\mathrm{eff}}$ receives contributions from all the quantized fields, bosons and fermions. Remarkably, there also exist higher powers $\mathcal{O}(H^6)$ which can trigger inflation in the early universe. Finally, the equation of state (EoS) of the vacuum receives also quantum corrections from bosons and fermion fields, shifting its value from -1. The striking consequence is that the EoS of the quantum vacuum may nowadays effectively appears as quintessence.

arXiv commentMatching the published version in EPJC. Work dedicated to Harald Fritzsch

References in corpus (86)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Planck 2015 results. XIII. Cosmological parameters
• The Cosmological Constant and Dark Energy
• Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies
• f(R) Theories Of Gravity
• Extended Theories of Gravity
• Cosmological Constant - the Weight of the Vacuum
• The Complete Light-curve Sample of Spectroscopically Confirmed Type Ia Supernovae from Pan-STARRS1 and Cosmological Constraints from The Combined Pantheon Sample
• A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• f(T) teleparallel gravity and cosmology
• Challenges for $\Lambda$CDM: An update
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Varying constants, Gravitation and Cosmology
• CDM Models with a Smooth Component
• Cosmology Intertwined II: The Hubble Constant Tension
• The Cosmological Constant is Back
• Cosmological constant and vacuum energy: old and new ideas
• First evidence of running cosmic vacuum: challenging the concordance model
• The Cosmological Evolution of the Nucleon Mass and the Electroweak Coupling Constants
• Smoothing Supernova Data to Reconstruct the Expansion History of the Universe and its Age
• Effective equation of state for dark energy: mimicking quintessence and phantom energy through a variable Lambda
• The $H_0$ tension in light of vacuum dynamics in the Universe
• Dark energy: a quantum fossil from the inflationary Universe?
• Expansion History with Decaying Vacuum: A Complete Cosmological Scenario
• Hints of dynamical vacuum energy in the expanding Universe
• Dynamical vacuum energy in the expanding Universe confronted with observations: a dedicated study
• Possible signals of vacuum dynamics in the Universe
• Complete Cosmic History with a dynamical Lambda(H) term
• A rapid transition of $G_{\mathrm{eff}}$ at $z_t\simeq 0.01$ as a solution of the Hubble and growth tensions
• Brans-Dicke gravity with a cosmological constant smoothes out $\Lambda$CDM tensions
• Running vacuum against the $H_0$ and ${\sigma }_8$ tensions
• Renormalizing the vacuum energy in cosmological spacetime: implications for the cosmological constant problem
• The $\bar{\Lambda }CDM$ cosmology: from inflation to dark energy through running $\Lambda$
• A $w-M$ phantom transition at $z_t<0.1$ as a resolution of the Hubble tension
• Dynamical dark energy versus $\Lambda =$const. in light of observations
• Density perturbations for running vacuum: a successful approach to structure formation and to the ${\sigma }_8$-tension
• Can late-time extensions solve the $H_0$ and ${\sigma }_8$ tensions?
• Cosmologies with a time dependent vacuum
• Hubble tension or a transition of the Cepheid SnIa calibrator parameters?
• Running vacuum in quantum field theory in curved spacetime: renormalizing ${\rho }_{vac}$ without $\sim m^4$ terms
• Zero-point quantum fluctuations and dark energy
• Adiabatic regularization and particle creation for spin one-half fields
• How Far Are We from the Quantum Theory of Gravity?
• Late-transition vs smooth $H(z)$ deformation models for the resolution of the Hubble crisis
• Gravitational and Chiral Anomalies in the Running Vacuum Universe and Matter-Antimatter Asymmetry
• Brans-Dicke cosmology with a $\Lambda$- term: a possible solution to $\Lambda$CDM tensions
• Adiabatic regularization for spin-1/2 fields
• Running vacuum in the Universe: phenomenological status in light of the latest observations, and its impact on the ${\sigma }_8$ and $H_0$ tensions
• Can dark energy be expressed as a power series of the Hubble parameter?
• Measuring the stability of fundamental constants with a network of clocks
• The Atoms Of Space, Gravity and the Cosmological Constant
• Renormalized stress-energy tensor for spin-1/2 fields in expanding universes
• Relaxing the ${\sigma }_8$-tension through running vacuum in the Universe
• Matter Non-conservation in the Universe and Dynamical Dark Energy
• The Road to Precision Cosmology
• Quantum Anomalies in String-Inspired Running Vacuum Universe: Inflation and Axion Dark Matter
• Big Bang Nucleosynthesis constraints on higher-order modified gravities
• Stringy-Running-Vacuum-Model Inflation: from primordial Gravitational Waves and stiff Axion Matter to Dynamical Dark Energy
• Equation of state of the running vacuum
• Running vacuum in the Universe and the time variation of the fundamental constants of Nature
• Inflationary physics and transplanckian conjecture in the Stringy Running-Vacuum-Model: from the phantom vacuum to the true vacuum
• Geometrization of light bending and its application to SdSw spacetime
• Effective equation of state for running vacuum: "mirage" quintessence and phantom dark energy
• Revising the observable consequences of slow-roll inflation
• The Dirac equation in general relativity, a guide for calculations
• Quantum Hair and Black Hole Information
• Adiabatic expansions for Dirac fields, renormalization, and anomalies
• Fundamental constants and cosmic vacuum: the micro and macro connection
• Remarks on the renormalization of primordial cosmological perturbations
• Questioning the $H_0$ tension via the look-back time
• Brans-Dicke cosmology mimicking running vacuum
• Vacuum fluctuations in a supersymmetric model in FRW spacetime
• The Effective Theory of Gravity and Dynamical Vacuum Energy
• Running couplings from adiabatic regularization
• Running vacuum versus Holographic dark energy: a cosmographic comparison
• The Dirac Equation and the Normalization of its Solutions in a Closed Friedmann-Robertson-Walker Universe
• Cosmological Constant Problem and Renormalized Vacuum Energy Density in Curved Background
• Brans-Dicke gravity: from Higgs physics to (dynamical) dark energy
• An Estimate of Λin Resummed Quantum Gravity in the Context of Asymptotic Safety
• Electroweak Vacuum Instability and Renormalized Vacuum Field Fluctuations in Friedmann-Lemaitre-Robertson-Walker Background
• Cosmological Evolution of the Higgs Boson's Vacuum Expectation Value
• Is "Dark Energy" a Quantum Vacuum Energy?
• Cosmological Constant and Vacuum Zero Point Energy in Black Hole Backgrounds
• Renormalization, running couplings and decoupling for the Yukawa model in curved spacetime

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• Running vacuum in the Universe: phenomenological status in light of the latest observations, and its impact on the ${\sigma }_8$ and $H_0$ tensions
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• Composite Dark Energy and the Cosmological Tensions
• Stringy Running Vacuum Model and current Tensions in Cosmology
• Running vacuum in Brans-Dicke theory: a possible cure for the ${\sigma }_8$ and $H_0$ tensions
• Oscillating dark energy in light of the latest observations and its impact on the Hubble tension
• Torsion at different scales: from materials to the Universe
• Cosmological constraints on time-varying cosmological terms: A study of FLRW universe models with $\Lambda (t)$CDM cosmology
• Signature flips in time-varying $\Lambda (t)$ cosmological models with observational data
• Running vacuum and H^4-inflation
• Quantum-Ordering Ambiguities in Weak Chern-Simons 4D Gravity and Metastability of the Condensate-Induced Inflation
• The dynamics of vacuum, gravity and matter: Implications on the fundamental constants
• Physical scale adiabatic regularization in cosmological spacetimes
• Charged Black Holes from Interacting Vacuum
• Scalar Perturbations in Nonsingular Universes from Interacting Vacuum
• The Hubble tension as an effect of the renormalization of fundamental constants and cosmological parameters
• Dynamical-System analysis of single-axion monodromy inflation with periodically-modulated potentials
• Background dynamics and observational constraints of flat and non-flat $\Lambda (t)$CDM models from $H(z)$ and DESI DR2 BAO measurements