Equation of state of the running vacuum

Abstract

Recent studies of quantum field theory in FLRW spacetime suggest that the cause of the speeding up of the universe is the running vacuum (RV). Appropriate renormalization of the energy-momentum tensor shows that the vacuum energy density is a smooth function of the Hubble rate and its derivatives: ${\rho }_{\mathrm{vac}}={\rho }_{\mathrm{vac}}(H,\dot{H},\ddot{H},...)$. This is because in QFT the quantum scaling of ${\rho }_{\mathrm{vac}}$ with the renormalization point turns into cosmic evolution with $H$. As a result, any two nearby points of the cosmic expansion during the standard FLRW epoch are smoothly related through $\delta {\rho }_{\mathrm{vac}}\sim \mathcal{O}(H^2)$. In our approach, what we call the `cosmological constant' $\Lambda$ is just the nearly sustained value of $8\pi G(H){\rho }_{\mathrm{vac}}(H)$ around (any) given epoch, where $G(H)$ is the running gravitational coupling. In the present study, after summarizing the main QFT calculations supporting the RV approach, we focus on the calculation of the equation of state (EoS) of the RV for the entire cosmic history within such a QFT framework. In particular, in the very early universe, where higher (even) powers ${\rho }_{\mathrm{vac}}\sim \mathcal{O}(H^N)$ ($N=4,6,\dots$) triggered inflation during a short period in which $H=$const, the vacuum EoS is very close to $w_{\mathrm{vac}}=-1$. This ceases to be true during the FLRW era, where it adopts the EoS of matter during the relativistic ($w_{\mathrm{vac}}=1/3$) and non-relativistic ($w_{\mathrm{vac}}=0$) epochs. Interestingly enough, we find that in the late universe the EoS becomes mildly dynamical and mimics quintessence, $w_{\mathrm{vac}}\gtrsim -1$. It finally asymptotes to $-1$ in the remote future, but in the transit the RV helps alleviating the $H_0$ and ${\sigma }_8$ tensions.

arXiv commentSlightly changed title. Extended discussion, references added. Accepted for publication in Eur.Phys.J. C

References in corpus (46)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Dynamics of dark energy
• The Cosmological Constant and Dark Energy
• f(R) Theories Of Gravity
• Extended Theories of Gravity
• The Case for a Positive Cosmological Lambda-term
• In the Realm of the Hubble tension $-$ a Review of Solutions
• Challenges for $\Lambda$CDM: An update
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Varying constants, Gravitation and Cosmology
• First evidence of running cosmic vacuum: challenging the concordance model
• The Cosmological Evolution of the Nucleon Mass and the Electroweak Coupling Constants
• Running G and Λat low energies from physics at M_X: possible cosmological and astrophysical implications
• Effective equation of state for dark energy: mimicking quintessence and phantom energy through a variable Lambda
• 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
• Possible signals of vacuum dynamics in the Universe
• Dynamical vacuum energy in the expanding Universe confronted with observations: a dedicated study
• Brans-Dicke gravity with a cosmological constant smoothes out $\Lambda$CDM tensions
• Symmetry Breaking and Time Variation of Gauge Couplings
• Running vacuum against the $H_0$ and ${\sigma }_8$ tensions
• Hubble expansion and structure formation in the "running FLRW model" of the cosmic evolution
• 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 $\Lambda$
• The Cosmological Constant Problem and Running Vacuum in the Expanding Universe
• 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
• Dynamical dark energy or variable cosmological parameters?
• Running vacuum in quantum field theory in curved spacetime: renormalizing ${\rho }_{vac}$ without $\sim m^4$ terms
• Vacuum models with a linear and a quadratic term in H: structure formation and number counts analysis
• Dynamical dark energy: scalar fields and running vacuum
• Brans-Dicke cosmology with a $\Lambda$- term: a possible solution to $\Lambda$CDM tensions
• Relaxing the ${\sigma }_8$-tension through running vacuum in the Universe
• Matter Non-conservation in the Universe and Dynamical Dark Energy
• 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
• 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
• Effective equation of state for running vacuum: "mirage" quintessence and phantom dark energy
• Fundamental constants and cosmic vacuum: the micro and macro connection
• A Time Variation of Proton-Electron Mass Ratio and Grand Unification
• Running couplings from adiabatic regularization
• Running vacuum versus Holographic dark energy: a cosmographic comparison
• Running gravitational couplings, decoupling, and curved spacetime renormalization

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• Running vacuum in QFT in FLRW spacetime: The dynamics of ${\rho }_{\mathrm{vac}}(H)$ from the quantized matter fields
• Observational Constraints on Dynamical Dark Energy Models
• Stringy Running Vacuum Model and current Tensions in Cosmology
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• 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
• Beyond $\Lambda$CDM: Exploring a Dynamical Cosmological Constant Framework Consistent with Late-Time Observations
• Running vacuum and H^4-inflation
• Quantum-Ordering Ambiguities in Weak Chern-Simons 4D Gravity and Metastability of the Condensate-Induced Inflation
• Does the Vacuum Gravitate on Microscopic Scales? Rydberg Atoms Indicate Probably Not
• Physical scale adiabatic regularization in cosmological spacetimes
• The dynamics of vacuum, gravity and matter: Implications on the fundamental constants
• Scale-dependent gravity and covariant scale-setting
• Antimatter Gravity Experiments, the Astronomical Challenges to Lambda-CDM Cosmology and the Quantum Vacuum as a Possible Source of Gravity in the Universe
• Background dynamics and observational constraints of flat and non-flat $\Lambda (t)$CDM models from $H(z)$ and DESI DR2 BAO measurements
• The Hubble tension as an effect of the renormalization of fundamental constants and cosmological parameters