Research Program Invitation

What If the Vacuum Gravitates Locally?

Separating Cosmic Expansion from Quantum Vacuum Energy

A Comprehensive Research Program Grounded in Known Physics

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

Institute of Integrative and Interdisciplinary Research, Toronto
Information Physics Institute, Gosport

Email: info@interdisciplinary-institute.org

Dear Colleague,

You are receiving this research program because your work has touched upon aspects of a fundamental question that cosmology must now confront: Is the identification of quantum vacuum energy with the cosmological constant necessary, or have we conflated two distinct phenomena?

The standard ΛCDM model rests on an assumption made by Zel’dovich in 1967—that the quantum vacuum energy density ρ_vac and the cosmological constant Λ are the same entity. This assumption has produced the most severe discrepancy in the history of physics (120 orders of magnitude) and has forced the introduction of exotic dark matter particles that remain undetected after forty years of searches.

This research program proposes a radical but simple alternative: separate them. More importantly, it proposes to do so using only physics we already know—general relativity, quantum field theory, the Standard Model, and $E = m c^{2}$ —without invoking new particles, new forces, or fine-tuned constants.

The central insight is this: the vacuum already has structure and energy (confirmed by the Higgs field, QCD condensates, and the fact that boundary conditions modify vacuum fluctuations). Energy is mass ( $E = m c^{2}$ E=mc2). Mass gravitates (general relativity). Therefore, whatever energy the vacuum possesses must gravitate. The only question is where its gravitational effects become observable. Our answer: locally, within bound structures where cosmic expansion is suppressed.

We invite you to consider how your own contributions point toward, or could be extended to, this framework—and to join us in developing what could be the first complete cosmological model built entirely on established physics.

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: Scientific Context — How Your Work Points Toward This Framework

Your own contributions have explored various aspects of this separation. Below, we show how diverse lines of inquiry converge on the hypothesis that vacuum energy gravitates locally—and suggest specific collaborative opportunities grounded in your established work.

3.1 The Cosmological Constant and False Vacua

S.M. Barr and D. Seckel have explored the possibility that our observed vacuum is a false vacuum, split from the true vacuum by Planck-suppressed operators [7]. They noted the coincidence: $Λ \sim M_{W}^{7} / M_{P l}^{3}$ Λ∼MW7/MPl3 suggests a connection to the weak scale.

In our framework, this “false vacuum” is precisely the local phase of vacuum energy—dense in the early universe, diluted today—while the true geometric Λ remains constant. The Barr-Seckel mechanism for generating small Λ from high-order effects becomes, in our interpretation, a description of how local vacuum energy evolves without affecting the geometric background.

Collaboration opportunity: Joint exploration of how false vacuum decay in the early universe could produce the high-density vacuum phase required for rapid structure formation (JWST observations). This uses only established QFT and cosmology.

3.2 Scale-Invariant Vacuum and MOND

Vesselin Gueorguiev and Andre Maeder’s Scale Invariant Vacuum (SIV) paradigm derives both dark energy and MOND-like phenomenology from scale invariance of the vacuum [8,9]. Their framework shows that the cosmological constant emerges naturally, and that the MOND acceleration parameter $a_{0}$ a0 appears at the correct order of magnitude.

Our “local gravitation” hypothesis provides a physical mechanism for the SIV’s scale-invariant vacuum: it is the phase-transitioned vacuum within galactic halos that produces the MOND-like behavior. The vacuum pressure gradient we derive: $F_{vac} = \frac{α c^{2}}{3} \nabla ρ_{m}$ Fvac=3αc2∇ρm

may be the microphysical origin of the MOND relation. This is not new physics—it is the gravitational effect of a known energy density gradient.

Collaboration opportunity: Derive the precise mapping between the SIV parameter space and our $α$ α coupling constant, testing against rotation curve data.

3.3 Gravitational Analog of Maxwell’s Equations

Richard J. Cook has demonstrated that the curvature equations—true and valid equations in conventional general relativity—do not suffer from the vacuum-energy problem [10]. The Einstein equation emerges as a first integral, and the cosmological constant appears as an integration constant unrelated to quantum vacuum energy.

This is precisely the mathematical foundation our framework requires: a rigorous demonstration that Λ and ρ_vac can be separate in the field equations themselves—within standard general relativity, not modified gravity.

Collaboration opportunity: Extend Cook’s curvature-equation formalism to include the bound/expanding vacuum distinction and derive the modified Poisson equation: $\nabla^{2} Φ = 4 π G (1 + 2 α) ρ_{m} - Λ_{0}$ ∇2Φ=4πG(1+2α)ρm−Λ0

from first principles.

3.4 Running Vacuum Models

Joan Solà’s running vacuum model (RVM) demonstrates that the vacuum energy density naturally evolves with the Hubble rate: $ρ_{vac} (H) = ρ_{vac}^{0} + ν H^{2}$ ρvac(H)=ρvac0+νH2 [11,12].

This is mathematically equivalent to our matter-dependent ansatz: $ρ_{vac} (ρ_{m}) = ρ_{vac, 0}^{bare} - α ρ_{m}$ ρvac(ρm)=ρvac,0bare−αρm

through the Friedmann equation. Solà’s QFT-based renormalization framework provides the microphysical foundation for a dynamical vacuum—exactly what our phenomenological model requires, and it arises from renormalization group methods in curved spacetime, not new physics.

Collaboration opportunity: Map the RVM parameter $ν$ ν to our spatial $α$ α, and use RVM’s success with $H_{0}$ H0 and $S_{8}$ S8 tensions to constrain our framework’s predictions for structure growth.

3.5 q-Theory and Dark Matter from Dark Energy

F.R. Klinkhamer and G.E. Volovik’s q-theory treats the quantum vacuum as a medium with conserved microscopic degrees of freedom [13]. They show that a small spacetime-dependent perturbation of the equilibrium q-field behaves gravitationally as a pressureless perfect fluid—making it a candidate for dark matter.

This is conceptually identical to our “bound vacuum” phase: the vacuum, when perturbed from equilibrium by the presence of matter, acquires gravitational properties matching dark matter. The q-theory is built on condensed matter analogies and established quantum field theory.

Collaboration opportunity: Develop the q-theory analog of our “phase transition” at the galactic boundary, and use their condensed-matter framework to derive the equation of state of bound vacuum.

3.6 Variable Cosmological Term and Dark Matter

Christian Henke has demonstrated that a variable cosmological term: $Λ (a) = Λ_{0} + Λ_{1} a^{- (4 - ϵ)}$ Λ(a)=Λ0+Λ1a−(4−ϵ)

can simultaneously solve the cosmological constant problem and generate an attractive force that explains dark matter [14]. The dynamical part of his $Λ (a)$ Λ(a) generates the missing mass—exactly as our gravitating vacuum component does.

His derivation from a Klein-Gordon equation for the scale factor provides a mathematical structure that may underpin our phase-transition mechanism, all within standard field theory.

Collaboration opportunity: Unify Henke’s scale-factor dynamics with our spatial $Λ (ρ_{m})$ Λ(ρm) ansatz to create a fully covariant description of vacuum phase transitions.

3.7 Generalized Continuum and Spacetime Torsion

Lalaonirina Rakotomanana models vacuum spacetime as a generalized continuum with curvature and torsion, showing that only gravitation and electromagnetism (as action-at-distance fields) are needed to describe dark energy and dark matter [15]. The torsion field replaces the ad hoc cosmological constant.

In our framework, the “bound vacuum phase” may correspond to a region of non-zero torsion induced by matter—a geometrization of the dark matter phenomenon within extended but classical general relativity.

Collaboration opportunity: Develop the Riemann-Cartan geometry of the void-galaxy boundary, where torsion from matter gradients may trigger the vacuum phase transition.

3.8 Phase Transitions and Dark Matter Relics

Daniel J.H. Chung and collaborators have shown that phase transitions in the early universe can leave imprints on dark matter relic abundance, with the vacuum energy during phase transitions affecting TeV-scale dark matter at the percent level [16].

Our framework proposes that these phase transitions continue to occur at galactic boundaries today—the “phase transition” between expanding and bound vacuum. The percent-level effects they calculate may become order-unity effects in our strongly-coupled regime, but still within known phase transition physics.

Collaboration opportunity: Model the galactic virial radius as a first-order phase transition surface, using Chung’s formalism to predict dark matter distribution profiles.

Part IV: 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.

Part I: 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

Part II: Theoretical Microphysics — Deriving the Vacuum-Matter Coupling

#	Title	Status	Basis in Known Physics
3	Matter-Dependent Vacuum Energy Density and Inhomogeneous Cosmic Expansion – A phenomenological approach	Сomplete	Running vacuum models, QFT in curved spacetime
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

Part III: 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

Part IV: 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	Outline only	Galactic dynamics, rotation curves, fluid mechanics
13	The Gravity of Emptiness – Cosmic voids as anchors of the filamentary network	Outline only	Large-scale structure, void dynamics, gravitational potential

Part V: 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	Outline only	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	Outline only	Stellar evolution, IMF, black hole demographics

Part VI: 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	Outline only	Chandrasekhar limit, stellar evolution, supernova physics
	Appendix A: Time and Calibration Problem — SNe Ia as a Test of Vacuum Evolution	Outline only	Statistical methods, survey science
	Appendix B: Observational Astrophysics — Searching for Baryonic Remnants and Cold Gas	Outline only	Radio astronomy, gravitational wave astronomy

Part VII: 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	Draft complete	Philosophy of science, Occam’s razor, history of cosmology

Part V: Observational and Experimental Connections

5.1 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.

5.2 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.

5.3 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 VII: Publication Plan

Paper Topic	Target Journal	Timeline
Foundational (1-2)	Foundations of Physics or Classical and Quantum Gravity	2025
Theoretical (3-6)	Physical Review D	2025-2026
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	2025

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

Part VIII: 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.
Virtual meeting: Discuss the framework and potential collaboration in more detail.
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.

Funding

The development of this research program is currently supported by internal resources of the Institute of Integrative and Interdisciplinary Research and the Information Physics Institute. We are actively seeking external funding for specific collaborative projects, particularly those involving numerical simulations and observational data analysis.

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.