Within the running vacuum model (RVM), grounded in quantum field theory in curved spacetime, the vacuum energy density ρvac = Λ/(8πG) depends on the Hubble parameter H and its derivatives: ρvac = ρvac(H, Ḣ, Ḧ, ...). In the present epoch, the evolution is extremely slow: δρvac ∼ O(mPl² H²), ensuring a dynamic dark energy. The gravitational constant G also varies, but only logarithmically: G = G(ln H). In the very early Universe, quantum fluctuations induce terms ∼ H⁴, triggering rapid inflation without the need for an inflaton field—this mechanism differs from Starobinsky inflation, where H is not constant. Thus, RVM provides a unified description of inflation and dark energy, and the dynamic vacuum aligns with the latest DESI data, which favors evolving dark energy over a static Λ.
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.
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.
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.
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 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.
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.
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.
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.
🎯 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.