v1 – Institute of Integrative and Interdisciplinary Research

Research Program: The Local Gravitation of Quantum Vacuum: A Unified Solution to the Dark Sector

Monograph. What If the Vacuum Gravitates Download

Kriger, B. (2026). The Local Gravitation of Quantum Vacuum: A Unified Solution to the Dark Sector. (αLGQV Theory Monograph). IIIR Cosmology and Theoretical Physics. https://doi.org/10.5281/zenodo.19027460

What If the Vacuum Gravitates Locally?

All article preprints completed to date are available in the table below.

Core Hypothesis

Quantum vacuum energy and the cosmological constant are physically distinct. The vacuum responds to local matter density through a single ansatz:

ρ_vac(ρ_m) = Λ₀ − α · ρ_m

The background Friedmann equation is identical to ΛCDM — the modification enters only through the Poisson equation in overdense regions. The observable universe expands exactly as in standard cosmology; structure grows differently.

The Coupling α Is Not a Free Parameter

Paper #3a derives α from finite-density QCD using three standard, experimentally verified ingredients: the Gell-Mann–Oakes–Renner relation, the in-medium chiral condensate shift, and the nucleon sigma terms (σ_π ≈ 50 MeV, σ_s ≈ 40 MeV). The chiral condensate is a Lorentz scalar, so its energy has equation of state w = −1 exactly — it is vacuum energy in the precise general-relativistic sense.

The bare QCD coupling is α = (σ_π + σ_s)/m_N ≈ 0.096. Two physical reductions apply: dark matter does not carry color charge (×0.156, Planck baryon fraction), and nonlinear screening confines the modification to the overdense volume fraction (÷3, from N-body simulations).

Predicted: α = 0.005. Observed: α = 0.003. Ratio: 1.7. No free parameters.

Key Discovery: Nonlinear Self-Screening

N-body simulations (Paper #9) revealed that the density-dependent modification G_eff = G(1+2α) automatically confines itself to the shrinking overdense volume fraction as structure grows. By z = 0, the modification is locked inside halos and filaments (~20–30% of the volume). The σ₈ enhancement is ~3× smaller than linear theory predicts.

This screening resolves the apparent tension between enhanced early growth (needed for JWST massive galaxies at z > 7) and moderate late-time σ₈ (needed for the S₈ tension): the same physics, the same constant α, different epochs.

Observational Consequences

The model makes one-parameter predictions testable with current and forthcoming data:

S₈ tension: α = −0.003 gives S₈ = 0.807, alleviating the ~3σ discrepancy between Planck and weak lensing surveys (Paper #8).
JWST massive galaxies: Positive α enhances the linear growth factor by 7–23% at z = 10, providing a mechanism for forming massive galaxies earlier than ΛCDM allows.
Void profiles: The model predicts deeper voids with thinner walls, distinguishable from f(R) and DGP gravity with DESI and Euclid data.
ISW signal: Enhanced ISW from voids due to unsuppressed vacuum energy in underdense regions.

Connection to the Running Vacuum Model

The RVM parameter ν in ρ_vac(H) = c₀ + νH² is related to the spatial coupling through ν ≈ −3α. The finite-density QCD derivation provides a physical mechanism for the running vacuum: the QCD condensate responds to matter density, and the response has vacuum equation of state.

Programme Structure

The programme consists of 17 papers spanning foundational theory, perturbation analysis, N-body simulations, void cosmology, elastic vacuum framework, and QFT derivations. The completed papers are listed below.

Part I: The Foundational Separation

The Core Hypothesis

The program rests on a single conceptual move: Λ and ρ_vac are physically distinct.

Quantity	Role	Basis
Λ (Cosmological Constant)	Geometry—a property of spacetime itself, constant and universal, governing homogeneous expansion	Einstein’s equations (1917)
ρ_vac (Quantum Vacuum Energy)	Field physics—the energy associated with quantum fields in their ground state	Higgs field vacuum expectation value (246 GeV), QCD condensates ( $⟨ \overset{ˉ}{q} q ⟩ \neq 0$ ⟨qˉq⟩=0), modification by boundary conditions (Casimir effect), phase transitions

Inside galaxies, where cosmic expansion is suppressed, vacuum energy contributes to gravitational mass—manifesting as dark matter. Outside, in voids, its gravity is compensated by expansion and remains unobservable.

This follows directly from three pillars of known physics:

The vacuum responds to boundary conditions — The Casimir effect demonstrates that modifying the vacuum produces measurable forces. Whether one interprets this via zero-point energy or as relativistic van der Waals forces [4], the key fact remains: the vacuum state is not invariant; it depends on the environment.
Energy is mass — $E = m c^{2}$ (Einstein, 1905).
Mass gravitates — general relativity (Einstein, 1915).

No new particles. No new forces. No fine-tuning. Only the consistent application of what we already know.

Part II: Why This Program Is Grounded in Known Physics

The crisis of modern cosmology is that 95% of the universe is said to consist of entities we have never detected—particles that do not exist in the Standard Model, and a vacuum energy that disagrees with quantum field theory by 120 orders of magnitude. This program argues that the crisis is not in the universe, but in our assumptions.

2.1 The Vacuum Is Measurable and Modifiable

The quantum vacuum is not an abstraction. Its properties have been measured:

Higgs field vacuum expectation value: $⟨ ϕ ⟩ \approx 246$ ⟨ϕ⟩≈246 GeV, confirmed by the Higgs boson mass.
QCD vacuum condensates: $⟨ \overset{ˉ}{q} q ⟩ \approx - (250 MeV)^{3}$ ⟨qˉq⟩≈−(250 MeV)3, measured through QCD sum rules and lattice calculations.
Casimir effect: Force between conducting plates, measured to sub-percent precision [1,3], demonstrating that boundary conditions modify the vacuum.
Phase transitions: The electroweak and QCD phase transitions changed the vacuum energy density by calculable amounts.

These are not theoretical predictions awaiting confirmation. They are measurements.

2.2 The Casimir Effect: What It Does and Does Not Tell Us

The Casimir effect is often cited as direct evidence for the reality of zero-point energy. However, as Robert Jaffe emphasized in his 2005 paper [4], this is not the only interpretation. Jaffe demonstrates that “Casimir effects can be formulated and Casimir forces can be computed without reference to zero-point energies. They are relativistic, quantum forces between charges and currents.” He concludes that “The Casimir force is simply the (relativistic, retarded) van der Waals force between the metal plates” [4].

This clarification is important, but it does not weaken our argument—it strengthens it. Whether one interprets the Casimir force as arising from zero-point energy modification or as a relativistic van der Waals force, the essential physical fact remains: the presence of material boundaries (matter) modifies the quantum vacuum state, and this modification produces measurable forces [1-3,5].

The Lifshitz theory provides a unified framework that encompasses both interpretations, describing dispersion forces as arising from fluctuating electromagnetic fields in media [2,5]. As Klimchitskaya, Mohideen, and Mostepanenko explain, “The physical origin of both the van der Waals and Casimir forces is connected with the existence of quantum fluctuations” [5]. The key point for cosmology is that the vacuum is not a fixed, unchangeable background—it responds to the presence of matter.

This is precisely what our framework requires: the vacuum energy density ρ_vac can be different in different environments. Inside a galaxy, where matter is abundant, the vacuum state is modified. Outside, in voids, it remains in its “free” state. The Casimir effect—however interpreted—demonstrates that such modification is real and measurable.

2.3 Gravitation Is Universal

General relativity admits no exception clause. The stress-energy tensor $T_{μ ν}$ Tμν sources the gravitational field, and it includes all forms of energy. If the vacuum has energy—whether we call it zero-point energy or the ground state energy of quantum fields—it must appear on the right-hand side of Einstein’s equations, not as geometry, but as source.

The only remaining question is how this source behaves in different environments. The Casimir effect teaches us that vacuum energy is environment-dependent. Our framework simply extends this lesson to cosmology.

2.4 Bound Systems Decouple from Expansion

It is standard physics that gravitationally bound systems (galaxies, clusters) do not participate in the Hubble flow [6]. Inside a galaxy, space does not expand. Therefore, any gravitational effect of vacuum energy that would be compensated by expansion in the void becomes uncompensated inside the galaxy.

This is the mechanism: vacuum energy gravitates everywhere, but its effects are only observable where expansion cannot cancel them.

2.5 Mathematical Validation: The QKDE Framework

The formal consistency of separating dark energy dynamics from the metric sector has been recently demonstrated in the Quantum-Kinetic Dark Energy (QKDE) framework (Brown, 2026). QKDE proves that it is mathematically possible to maintain an unmodified Einstein-Hilbert sector , while treating dark energy as a result of a time-dependent scalar kinetic normalization. This provides the rigorous, iteration-free numerical framework required for our program, validating that such a separation does not violate diffeomorphism invariance and remains consistent with General Relativity at machine precision

Reference:

Brown, D. (2026). Quantum-Kinetic Dark Energy (QKDE): An effective dark energy framework with a covariantly completed time-dependent scalar kinetic normalization. International Journal of Modern Physics D, 35(4), 2650006. [doi:10.1142/S0218271826500069]

Part III: The Complete Research Program

The full program comprises 17 papers organized into seven parts, each exploring a different aspect of the framework. All are built on established physics.

Foundations — The Central Hypothesis

#	Title	Status	Basis in Known Physics
1 1a	On Quantum Vacuum Energy, Cosmological Constant and Missing Mass – Asking the right questions Theoretical Separation of Quantum Vacuum Energy from the Cosmological Constant: A Review of Foundational Approaches	Сomplete Сomplete	History of physics, Zel’dovich (1967) identification Unimodular gravity, Kaloper–Padilla sequestering, Volovik condensed-matter analogy, running vacuum models (Solà Peracaula), the QKDE numerical framework (Brown, 2026) for covariant scalar kinetic normalization., Rugh–Zinkernagel foundational critique
2	What If the Vacuum Gravitates Locally? – Separating Cosmic Expansion from Quantum Vacuum Energy	Сomplete	General relativity, $E = m c^{2}$ E=mc2, quantum field theory

Theoretical Microphysics — Deriving the Vacuum-Matter Coupling

#	Title	Status	Basis in Known Physics
3 3a	Matter-Dependent Vacuum Energy Density and Inhomogeneous Cosmic Expansion – A phenomenological approach The Vacuum–Matter Coupling from Finite-Density QCD: Sigma Terms, Chiral Condensate, and the Origin of α	Сomplete Сomplete	Running vacuum models, QFT in curved spacetime finite-density QCD
4	A Microscopic Model for the Dependence of Vacuum Energy on Matter Density – Towards a quantum field theory derivation	Сomplete	Renormalization group, effective actions, Casimir effect
5	The Elastic Vacuum – A Sequestering Mechanism for Vacuum Energy and the Complete Dynamical History of Cosmic Expansion	Сomplete	General relativity, E = mc², LIGO (gravitational waves), Sakharov induced gravity, trace-free Einstein equations (Ellis), Casimir effect, Kaloper–Padilla sequestering, bound system decoupling

Cosmological Consequences — From Inflation to Large-Scale Structure

#	Title	Status	Basis in Known Physics
6	Connection of Vacuum Energy with Inflation: The Elastic Potential, Initial Conditions, and the Origin of Primordial Fluctuations	Сomplete	Inflationary cosmology, quantum fluctuations
7	CMB Compatibility and the Dissolution of the Mass Hierarchy in the Elastic Vacuum	Сomplete	CMB physics, Boltzmann equations, acoustic oscillations
8	Structure Growth in the Gravitating Vacuum Model – Modified perturbation equations and the S₈ tension	Сomplete	Linear perturbation theory, growth factor
9	N-body Simulations with a Gravitating Vacuum Phase – Testing the model against structure formation	Сomplete	Numerical cosmology, simulation codes

Galactic and Astrophysical Manifestations — From First Stars to Rotation Curves

#	Title	Status	Basis in Known Physics
10	Known Properties of Vacuum Energy, Dark Matter and JWST Early Galaxy Formation – A unified view	Сomplete	Stellar evolution, galaxy formation, JWST observations
11	Two Pathways of Primordial Cloud Collapse – Fragmentation versus direct collapse under enhanced vacuum energy	Сomplete	Jeans instability, Bonnor-Ebert mass, star formation
12	The Vacuum Capture Model – Phase transitions and galactic rotation without dark matter	Сomplete	Galactic dynamics, rotation curves, fluid mechanics
13	The Gravity of Emptiness: Cosmic Voids as Attractors of the Filamentary Network in the Block Universe	Сomplete	Large-scale structure, void dynamics, gravitational potential

The Hidden Baryonic Sector — Compact Remnants and Cold Gas

#	Title	Status	Basis in Known Physics
14	Invisible Gas as a Major Component of the Missing Mass – Fractal cold gas in galactic halos	Сomplete	ISM physics, fractal models, radio astronomy
15	Mass of Compact Remnant Population in the Milky Way – Accounting for direct collapse black holes over 13 billion years	Сomplete	Stellar evolution, IMF, black hole demographics

Precision Tests — Supernovae and the Hubble Tension

#	Title	Status	Basis in Known Physics
16	Type Ia Supernovae in a High-Density Vacuum Cosmology – Revisiting the Chandrasekhar limit and distance calibration	Сomplete	Chandrasekhar limit, stellar evolution, supernova physics

Philosophical Synthesis — The Copernican Conclusion

#	Title	Status	Basis in Known Physics
17	Block Universe, The Copernican Principle and the End of Anthropocentrism in Cosmology – Why the vacuum gravitating is more elegant than exotic particles	Сomplete	Philosophy of science, Occam’s razor, history of cosmology

Part IV: Observational and Experimental Connections

4.1 CMB and Large-Scale Structure

The framework predicts that vacuum energy does not enter the Friedmann equation—it is sequestered from cosmological dynamics while remaining gravitationally active inside bound structures. This preserves the CMB acoustic peak structure exactly as observed. The Integrated Sachs-Wolfe effect, however, should show enhancement from void growth, potentially explaining anomalies in CMB cold spot correlations.

Testable prediction: Enhanced ISW signal from voids, correlated with void catalogs from DESI and Euclid.

4.2 Supernovae and Distance Calibration

Type Ia supernovae remain standard candles because the Chandrasekhar limit is unaffected by direct vacuum pressure (fractional change $\sim 10^{- 28}$ ∼10−28). However, indirect effects on progenitor evolution may produce small redshift-dependent luminosity corrections at the $ϵ \ln (1 + z)$ ϵln(1+z) level with $ϵ \sim 0.01 - 0.02$ ϵ∼0.01−0.02—testable with LSST, Roman, and Euclid.

Testable prediction: Redshift-dependent residuals in Hubble diagram, correlated with host galaxy properties.

4.3 Direct Detection: Gas and Remnants

The baryonic components of missing mass—fractal cold gas and compact remnants—are detectable with next-generation facilities:

Facility	Target	Observable
ngVLA	Cold fractal gas	Molecular absorption lines at $\sim 3$ ∼3 K, line widths $\sim 0.1$ ∼0.1 km/s
SKA	Gas in halos	HI absorption, FRB dispersion measures
LISA	Compact remnants	Merger rates of $10 - 10^{3} M_{⊙}$ 10−103M⊙ black holes at $\sim 10^{- 5} {yr}^{- 1}$ ∼10−5 yr−1 per galaxy
Roman	Compact remnants	Microlensing events toward Andromeda

Testable prediction: Specific signatures that distinguish baryonic remnants from primordial black holes and particle dark matter.

Part VI: How You Could Contribute

Research Area	Potential Contribution	Relevant Papers
Quantum Field Theory in Curved Spacetime	Derive $ρ_{vac} (ρ_{m})$ ρvac(ρm) from first principles; calculate renormalized stress-energy tensor in bound systems	#4 (Microscopic Model)
General Relativity and Modified Gravity	Develop curvature-equation formalism with phase-transition boundary conditions	#2 (Foundational), #5 (Sequestering)
Cosmological Simulations	Implement N-body codes with cell-dependent vacuum energy; compare to ΛCDM	#9 (N-body Simulations)
Observational Cosmology	Test predictions with CMB, supernova, and large-scale structure data	#7 (CMB), #16 (Supernovae)
Particle Phenomenology	Connect to axion, q-theory, and other vacuum-based dark matter models	#4 (Microscopic), #12 (Vacuum Capture)
Astrophysics	Search for fractal gas and compact remnants with ngVLA, SKA, LISA	#14 (Gas), #15 (Remnants)

Part V: Publication Plan

Paper Topic	Target Journal	Timeline
Foundational (1-2)	Foundations of Physics or Classical and Quantum Gravity	2026
Theoretical (3-6)	Physical Review D	2026-2027
Cosmological (7-9)	Journal of Cosmology and Astroparticle Physics	2026
Astrophysical (10-13)	Astrophysical Journal or Monthly Notices of the RAS	2026
Observational (14-16)	Astronomy & Astrophysics or Physical Review Letters	2026-2027
Philosophical (17)	Studies in History and Philosophy of Modern Physics	2026

All papers will be made available on arXiv prior to submission. Co-authorship follows standard academic practice: significant intellectual contributions warrant co-authorship.

Part VI: Next Steps

If any of these opportunities interest you, I would be delighted to discuss further:

Expression of interest: Reply indicating which paper(s) you might contribute to.
Draft exchange: Share existing drafts for your review and feedback.
Joint development: Begin work on specific derivations, calculations, or observational strategies.

Conclusion: Grounding Cosmology in Known Physics

The identification of Λ with ρ_vac was made in 1967, assumed without proof, and has produced a 120-order crisis. The framework proposed here—What If the Vacuum Gravitates Locally?—offers a way out by recognizing that these are different quantities doing different jobs.

Crucially, this framework uses only physics we already know:

The vacuum is modifiable by matter — demonstrated by the Casimir effect, whether interpreted via zero-point energy or as relativistic van der Waals forces [1-5].
Energy is mass — $E = m c^{2}$ E=mc2.
Mass gravitates — general relativity.
Bound systems decouple from expansion — standard cosmology [6].

No new particles. No new forces. No fine-tuning. Only the consistent application of what we have known for a century.

The Casimir effect does not prove the absolute magnitude of vacuum energy, but it does prove that the vacuum state depends on boundary conditions [1-5]. Our framework extends this principle to cosmology: the vacuum inside a galaxy (where matter provides the “boundary conditions”) differs from the vacuum in empty space. That difference, by $E = m c^{2}$ E=mc2 and general relativity, produces gravitational effects that we observe as dark matter.

Your work has already contributed essential pieces to this puzzle. We invite you to consider whether your insights might find a natural home in this larger synthesis—and whether the questions raised here are worth pursuing together.

The universe may be simpler than we have allowed ourselves to imagine. Perhaps the vacuum, which we already know responds to matter, simply does what Einstein taught us: energy is mass, and mass gravitates. The only remaining question is where.

We look forward to hearing from you.

References

[1] Casimir, H.B.G. (1948). On the attraction between two perfectly conducting plates. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, 51, 793-795.

[2] Lifshitz, E.M. (1956). The theory of molecular attractive forces between solids. Soviet Physics JETP, 2, 73-83.

[3] Lamoreaux, S.K. (1997). Demonstration of the Casimir force in the 0.6 to 6 μm range. Physical Review Letters, 78, 5-8.

[4] Jaffe, R.L. (2005). Casimir effect and the quantum vacuum. Physical Review D, 72, 021301. [“The Casimir force is simply the (relativistic, retarded) van der Waals force between the metal plates” — demonstrating that the effect does not require zero-point energy interpretation.]

[5] Klimchitskaya, G.L., Mohideen, U., & Mostepanenko, V.M. (2009). The Casimir force between real materials: Experiment and theory. Reviews of Modern Physics, 81, 1827-1885. [Unified treatment of dispersion forces via Lifshitz theory.]

[6] Carrera, M., & Giulini, D. (2010). Influence of global cosmological expansion on local dynamics and kinematics. Reviews of Modern Physics, 82, 169-208. [Bound systems decouple from Hubble flow.]

[7] Barr, S.M., & Seckel, D. (1992). The cosmological constant and the weak scale. Physical Review D, 46, 539-549.

[8] Maeder, A. (2017). An alternative to the ΛCDM model: The case of scale invariance. The Astrophysical Journal, 834, 194.

[9] Gueorguiev, V., & Maeder, A. (2020). Scale-invariant dynamics and the cosmological constant. Symmetry, 12, 1089.

[10] Cook, R.J. (2022). Gravitational curvature equations and the cosmological constant. General Relativity and Gravitation, 54, 45.

[11] Solà, J. (2013). Cosmological constant and vacuum energy: Old and new ideas. Journal of Physics: Conference Series, 453, 012015.

[12] Solà Peracaula, J., de Cruz Pérez, J., & Gómez-Valent, A. (2017). Dynamical dark energy vs. Λ = const in light of observations. Europhysics Letters, 121, 39001.

[13] Klinkhamer, F.R., & Volovik, G.E. (2008). q-theory and dark matter. JETP Letters, 88, 289-294.

[14] Henke, C. (2025). Variable cosmological term and dark matter from a Klein-Gordon scale factor. Classical and Quantum Gravity, forthcoming.

[15] Rakotomanana, L. (2023). Vacuum spacetime as a generalized continuum with torsion. International Journal of Geometric Methods in Modern Physics, 20, 2350098.

[16] Chung, D.J.H., et al. (2024). Phase transitions and dark matter relic abundance. Physical Review D, 109, 023521.