Running Vacuum in the Expanding Universe: A Unified Quantum Field Paradigm of Inflation and Dark Energy ✛ ✎ ✦
Context
As early as 1934, Georges Lemaître linked the cosmological constant to vacuum energy, and the expansion of the universe discovered by Edwin Hubble raised the question of this energy's nature. However, modern quantum field theory predicts a contribution from vacuum fluctuations many orders of magnitude larger than the observed value of dark energy. This discrepancy, known as the cosmological constant problem, requires accounting for spacetime curvature and a consistent description of vacuum energy in cosmology.
Methods
The RVM employs an off-shell adiabatic renormalization procedure in an expanding universe, where the renormalization scale M is identified with the Hubble parameter H. This allows expressing the renormalized vacuum energy density (VED) as a function of H and its derivatives: $ρ_{vac}$ = $ρ_{vac}$(H, ̇H, ̈H, …). Calculations are performed in the Friedmann–Lemaître–Robertson–Walker metric for a non-minimally coupled scalar field, then extended to Standard Model and Grand Unification fields.
Results
It turns out that in the early universe, the ∼$H^4$ term drives inflation without invoking an inflaton field, solving the horizon problem and the vast entropy of the observable universe. In the current epoch, the leading ∼$m^{2H}^2$ term yields a smooth evolution of dark energy density, consistent with recent data from the DESI survey and the cosmic microwave background. Moreover, the model predicts a logarithmic drift of the gravitational constant, echoing Paul Dirac's idea of possible variation of fundamental constants.
Implications
The dynamic nature of the vacuum in RVM helps alleviate contemporary cosmological tensions, including the dark matter and large-scale structure problem (the σ8 tension). A variable cosmological constant and slowly changing gravitational coupling pave the way for a unified description of cosmic evolution without resorting to hypothetical quintessence fields.
Future development
Future research will aim to incorporate quantum-gravity corrections and string theory effects (StRVM), as well as to perform more detailed comparisons with data from upcoming surveys like Euclid and the Roman Space Telescope. High-precision measurements of the Hubble constant and structure growth are expected to distinguish between RVM and the static ΛCDM predictions.
Impact
The running vacuum paradigm impacts not only cosmology but also particle physics, predicting cosmic drifts of constants such as the fine-structure constant and particle masses. These predictions can be tested in laboratory experiments with ultra-precise atomic clocks.
Next steps
It is necessary to perform a full two-loop renormalization analysis within RVM including all Standard Model fields, and to develop a consistent theory of cosmological perturbations for a dynamic vacuum. In parallel, a Bayesian model comparison using the latest supernova and baryon acoustic oscillation data is planned.
Key open problems
RVM offers a natural solution to the cosmological constant problem by canceling ∼m^4 contributions through renormalization, leaving only mild ∼m^2H^2 terms. This links macroscopic cosmology with microscopic quantum field theory and can shed light on the nature of dark energy and inflation.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The paper examines the running vacuum model (RVM), in which the vacuum energy density depends on the Hubble parameter and its derivatives through adiabatic renormalization off the mass shell. It is shown that in the early Universe, a contribution ∼H⁴ causes inflation without an inflaton field, while in the modern epoch, a contribution ∼m²H² yields a smooth dark energy evolution consistent with DESI data. A logarithmic drift of the gravitational constant is also predicted.
Where its strength is
The strength of the work lies in its unified description of inflation and dark energy based on quantum field effects in curved spacetime, without introducing hypothetical fields. This provides a natural link between early and late cosmology and concrete predictions for the evolution of vacuum energy.
Where it could go next
- It might be interesting to compare RVM predictions with models where dark energy changes sign, to see whether vacuum dynamics allows such a transition.based on: Dark Energy That Changes Sign arXiv:2606.01360
- A related approach links inflation and dark energy through a Goldstone boson; one could compare the mechanisms of inflation generation and vacuum evolution.based on: Awakening a Sleeping Actor: How a Goldstone Boson Links Inflation and Dark Energy arXiv:2607.16405v1
- Our archive contains a work on vacuum decay that gave rise to the Big Bang; one could consider how the initial conditions for the RVM align with such a scenario.based on: Dark Start: How Vacuum Decay Birthed the Big Bang arXiv:2606.06587v1
Worth trying
- Test whether the RVM can reproduce a sign change in dark energy, as in phantom-crossing models.
- Compare predictions for the primordial perturbation spectrum in the RVM and in a model with a Goldstone boson.
- Investigate how the decay of the initial vacuum state affects the initial conditions for H and its derivatives in the RVM.
Why this may matter
If the RVM can be connected to alternative mechanisms of inflation and dark energy dynamics, it would strengthen its status as a unified quantum field paradigm and may point to new observational signatures.
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The archive is crowded around this work: 5 reviews nearby, closest at 0.72. This ground is well walked — and there is plenty to compare against.
Although the zero-point fluctuations of the electromagnetic field in flat space are infinite, in curved spacetime they yield a finite and measurable contribution to the cosmological constant — about 10⁻⁴⁷ GeV⁴. Ironically, it is gravity that creates the cosmological constant problem, yet also points the way to its solution.
In Greg Egan's novel 'Quarantine', the cosmological constant is controlled by observers, resonating with the idea of a dynamic vacuum sensitive to the state of the universe.
Key numbers
- Vacuum energy density today: ∼10⁻⁴⁷ GeV⁴
- Parameter ν_eff (strength of VED evolution): 10⁻⁴ – 10⁻³
- Hubble parameter today H_0: ∼10⁻⁴² GeV
- Planck mass m_Pl: ≈1.22×10¹⁹ GeV
- Post-inflation temperature T_max: ≤ 0.1 m_Pl ~ 10¹⁸ GeV