Zero-point quantum fluctuations and dark energy

Abstract

In the Hamiltonian formulation of General Relativity the energy associated to an asymptotically flat space-time with metric $g_{\mu \nu }$ is related to the Hamiltonian $H_{GR}$ by $E=H_{GR}[g_{\mu \nu }]-H_{\mathrm{GR}}[{\eta }_{\mu \nu }]$, where the subtraction of the flat-space contribution is necessary to get rid of an otherwise divergent boundary term. This classic result indicates that the energy associated to flat space does not gravitate. We apply the same principle to study the effect of zero-point fluctuations of quantum fields in cosmology, proposing that their contribution to the cosmic expansion is obtained computing the vacuum energy of quantum fields in a FRW space-time with Hubble parameter $H(t)$ and subtracting from it the flat-space contribution. [...] After renormalization, this produces a renormalized vacuum energy density $\sim M^2{H}^2(t)$, where $M$ is the scale where quantum gravity sets is, so for $M$ of order of the Planck mass a vacuum energy density of the order of the critical density can be obtained without any fine tuning. The counterterms can be chosen so that the renormalized energy density and pressure satisfy $p=w\rho$, with $w$ a parameter that can be fixed by comparison to the observed value, so in particular one can chose $w=-1$. An energy density evolving in time as $H^2(t)$ is however observationally excluded as an explanation for the dominant dark energy component which is responsible for the observed acceleration of the universe. We rather propose that zero-point vacuum fluctuations provide a new subdominant "dark" contribution to the cosmic expansion that, for a UV scale $M$ slightly smaller than the Planck mass, is consistent with existing limits and potentially detectable.

16 pages, 1 figure; v3: conceptual improvements. References added. To appear in Phys. Rev. D

References in corpus (26)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Dynamics of dark energy
• The Cosmological Constant and Dark Energy
• Cosmological Constant - the Weight of the Vacuum
• Phenomenology, Astrophysics and Cosmology of Theories with Sub-Millimeter Dimensions and TeV Scale Quantum Gravity
• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Effective Field Theory, Black Holes, and the Cosmological Constant
• Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation
• Entropy Bounds and Dark Energy
• Relic neutrino decoupling including flavour oscillations
• Primordial Nucleosynthesis: from precision cosmology to fundamental physics
• On the possible running of the cosmological "constant"
• The scaling evolution of cosmological constant
• Effective Action of Vacuum: Semiclassical Approach
• Holography and Variable Cosmological Constant
• Hubble expansion & Structure Formation in Time Varying Vacuum Models
• Variable Cosmological Constant as a Planck Scale Effect
• Dark energy: a quantum fossil from the inflationary Universe?
• A cosmological constant from the QCD trace anomaly?
• Testing the running of the cosmological constant with Type Ia Supernovae at high z
• LXCDM: a cosmon model solution to the cosmological coincidence problem?
• Vacuum Fluctuations of Energy Density can lead to the observed Cosmological Constant
• Dark energy perturbations and cosmic coincidence
• Dynamically avoiding fine-tuning the cosmological constant: the "Relaxed Universe"
• Composite dark energy: cosmon models with running cosmological term and gravitational coupling
• On the scaling rules for the anomaly-induced effective action of metric and electromagnetic field

Cited by in corpus (57)

• Cosmological constant and vacuum energy: old and new ideas
• Dynamical vacuum energy in the expanding Universe confronted with observations: a dedicated study
• Implications, consequences and interpretations of generalized entropy in the cosmological setups
• Generalizing the running vacuum energy model and comparing with the entropic-force models
• More on QCD Ghost Dark Energy
• 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 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
• Early dark energy from zero-point quantum fluctuations
• The scalar bi-spectrum in the Starobinsky model: The equilateral case
• Topological Susceptibility and Contact Term in QCD. A Toy Model
• Entropy, Contact Interaction with Horizon and Dark Energy
• Effective Potential in Curved Space and Cut-Off Regularizations
• Entropic Force Scenarios and Eternal Inflation
• Running vacuum in QFT in FLRW spacetime: The dynamics of ${\rho }_{\mathrm{vac}}(H)$ from the quantized matter fields
• Cosmological constraints on the Generalized Uncertainty Principle from modified Friedmann equations
• Confronting the relaxation mechanism for a large cosmological constant with observations
• Contribution of the hybrid inflation waterfall to the primordial curvature perturbation
• Zero-point quantum fluctuations in cosmology
• Deviation from the Standard Uncertainty Principle and the Dark Energy Problem
• Inflaton as an auxiliary topological field in a QCD-like system
• Galaxy cluster angular size data constraints on dark energy
• Vacuum fluctuations in a supersymmetric model in FRW spacetime
• Vacuum energy as dark matter
• Casimir Dark Energy, Stabilization of the Extra Dimensions and Gauss-Bonnet Term
• Cosmological Constant Problem and Renormalized Vacuum Energy Density in Curved Background
• Sounds of instability from generalized QCD ghost dark energy
• Scrutinizing the Cosmological Constant Problem and a possible resolution
• Casimir scaling in gauge theories with a gap. Deformed QCD as a toy model
• Dynamical de Sitter phase and nontrivial holonomy in strongly coupled gauge theories in expanding Universe
• QCD modified ghost scalar field dark energy models
• Thermodynamic of universe with a varying dark energy component
• Effective cosmological constant induced by stochastic fluctuations of Newton's constant
• Cosmological Perturbations and the Running Cosmological Constant Model
• Generalized Uncertainty Principle mimicking dynamical Dark Energy: matter perturbations and gravitational wave data analysis
• Vacuum fluctuations of the supersymmetric field in curved background
• Vacuum stress-tensor in SSB theories
• The large-scale structure of vacuum
• String-Inspired Running Vacuum, the "Vacuumon", and the Swampland Criteria
• Energy stored on a cosmological horizon and its thermodynamic fluctuations in holographic equipartition law
• Relaxing a large cosmological constant in the astrophysical domain
• Topological Inflation
• Dark energy and dimensional transmutation in $R^2$ gravity
• Quantum Yang--Mills Dark Energy
• Late time cosmic acceleration from natural infrared cutoff?
• Higgs effective potential in a perturbed Robertson-Walker background
• Thermodynamic analysis of universes with the initial and final de-Sitter eras
• On the Effective Equation of State of Dark Energy
• Revisiting regularization with Kaluza-Klein states and Casimir vacuum energy from extra dimensional spaces
• Second-order effective energy-momentum tensor of gravitational scalar perturbations with perfect fluid
• Quantum origin of suppression for vacuum fluctuations of energy
• The effect of de Sitter like background on increasing the zero point budget of dark energy
• Supersymmetric dark energy
• Ultraviolet sensitivity of the cosmological sequester
• A New Strategy For Solving Two Cosmological Problems in Hadron Physics
• Spontaneous Symmetry Breaking Vacuum Energy in Cosmology