The project began with a single question: could the open puzzles in gravity — including dark matter and dark energy — be explained by a quantum vacuum response to the matter and curvature around it? That one question produced two distinct research programs. Both are summarized here; each card links to its full section below.
The cosmological constant is reframed as a horizon-information equilibrium phenomenon rather than a vacuum-energy sum awaiting cancellation. The framework has compressed aggressively — most early ideas were rejected — and now produces a candidate falsifiable observable: a "horizon-lock" redshift at z ≈ 0.5.
Read the full program → Program 2 · The galactic-scale workThe galaxy work succeeded cleanly. The Radial Acceleration Relation emerged naturally from vacuum coherence ideas; SPARC fits improved consistently. But the same formulation broke at the cluster scale — the Bullet Cluster could not be reproduced by a vacuum response coupled only to baryons. That failure forced a real conceptual pivot.
Read the full program →A research framework, not a finished theory. Several major derivations remain open in both programs, and the work has not undergone formal peer review.
The more fundamental branch. The framework has compressed aggressively: most early ideas were rejected, and what remains is a small set of structural results — a relative-entropy spine, a reduced horizon phase space, a modular/Fisher geometry, and a candidate falsifiable observable at z ≈ 0.5. Honest self-assessment: roughly 70–85% of the way from conceptual architecture toward publishable GR-level cosmological theory.
The cosmological constant is not a vacuum-energy sum. It is a horizon balance.
The cosmological constant problem is one of the largest gaps in physics: quantum field theory predicts a vacuum energy density roughly 122 orders of magnitude larger than what observation measures. The traditional question — "what cancels the huge predicted vacuum energy down to its tiny observed value?" — has no satisfying answer. The fine-tuning required is enormous; the anthropic explanation is unfalsifiable; supersymmetry on its own does not close the gap.
This program asks a different question. What if the cosmological constant isn't a vacuum-energy sum at all? What if it's the equilibrium between an evolving universe and a fundamental boundary — the cosmological horizon?
The cosmological horizon defines a finite causal patch. Information beyond it cannot influence us. The framework treats Λ as the balance between the evolving state inside our patch and the asymptotic de Sitter state at the horizon. That reframe — moving from "vacuum energy sum" to "horizon information equilibrium" — is the central conceptual move. From it, a concrete observational signature follows: a "horizon-lock" redshift around z ≈ 0.5.
A small set of structural objects, in compressed form.
The core principle. Λ emerges from finite causal-patch horizon completion. The cosmological constant is the equilibrium signature of a finite horizon-bounded information system, not a vacuum-energy integral.
The spine equation. The central dynamical object is the relative entropy between the evolving FRW causal-patch state and the asymptotic de Sitter equilibrium state:
This object — relative entropy between the time-dependent FRW state ρ(t) and the de Sitter equilibrium state σdS — is the spine of the framework. Everything else hangs off it.
Reduced horizon phase space. Using spherical FRW symmetry, the Hamiltonian constraint reduction, and a null-boundary / corner symplectic structure, the bulk FRW dynamics collapse away, leaving a reduced horizon sector. The surviving phase space is two-dimensional:
The surviving physical system is no longer the entire universe, nor the full QFT vacuum — it is a reduced horizon information system. This is the load-bearing structural result.
Modular and Fisher geometry. The reduced horizon system behaves like a 2D modular / Fisher phase space. The compatibility condition G(u,v) = ΩH(u, Jv) at leading order yields:
Earlier versions treated these normalizations as heuristic. They now emerge naturally from reduced symplectic structure plus modular compatibility plus Fisher isotropy — a real upgrade in rigor.
The observable. Switching from raw enclosed mass to a modularly-weighted matter-energy functional — with weight √(1 − r²/R∞²) from the de Sitter static-patch modular vector — gives a balance condition between modular energy and horizon entropy:
With fiducial flat ΛCDM values (Ωm ≈ 0.315, ΩΛ ≈ 0.685), this balance occurs at zlock ≈ 0.5. That redshift was not imposed — it emerged from independently computed modular-energy and horizon-entropy terms. It is currently the strongest candidate observational signal in the theory.
A long list of rejected routes. The framework compressed instead of expanding.
This branch grew from the same starting premise as the dark matter work — that the vacuum responds to matter and curvature, and that the answers to gravity's open puzzles might lie in characterizing that response correctly. For dark energy specifically, that initially meant chasing a cancellation mechanism for the predicted vacuum energy. None of the cancellation routes worked. What did work, eventually, was a complete reframe: the cosmological constant is not a vacuum-energy sum awaiting cancellation — it is an information-equilibrium condition at the cosmological horizon.
Most ideas tried along the way failed, and those failures sharpened what remains. The rejected routes include naive vacuum-energy cancellation, pure horizon-area entropy locking, guessed history-capacity integrals, purely baryonic-response cluster gravity, simple entropy-only inflection conditions, and raw mass closure without modular weighting.
The surviving structures are far fewer: a relative-entropy spine, a reduced horizon phase space, a modular / Fisher geometry, a CLPW-compatible Type II1 operator-algebra structure, and a modularly-weighted horizon-lock condition.
Three breakthroughs in particular made the framework what it is now:
Earlier in the project, essentially everything was open — the ontology, the equations, the dynamics, the observables. Now almost all remaining work is concentrated into a handful of technical theorem / proof / validation tasks. That compression — from speculative cosmology to mathematically structured candidate theory — is itself the main accomplishment.
Five sharply isolated frontiers. Each is theorem-proving rather than concept-inventing.
Closing the framework now requires five things, in order of difficulty:
The remaining work is no longer about inventing new concepts or adding new mechanisms. It is theorem proving, operator closure, generalized entropy completion, and observational hardening. That is what late-stage theory development is supposed to look like. The remaining fraction is the hardest part — but it is also the narrowest and most sharply defined part, and that is a very good sign.
A program investigating whether the gravity attributed to dark matter is, at galactic scales, a property of the vacuum responding to baryonic matter. Honest summary: the galaxy work succeeded, the cluster formulation failed, and the program eventually moved away from "gravity replacement" as a framing.
The vacuum responds to mass. Galaxies make the response coherent.
The starting question for the whole project was broader: could the open puzzles in gravity — dark matter and dark energy among them — be a single vacuum-response phenomenon, with the vacuum reacting to the matter and curvature around it? The galaxy work was the first concrete test of that idea. Inside ordered, slow-moving galactic systems, a vacuum coherence response reproduced the famous Radial Acceleration Relation — a tight empirical law that has resisted clean explanation under standard dark matter halos.
Cluster mergers like the Bullet Cluster told a different story. Lensing peaks displaced from the shocked gas cannot be reproduced by a vacuum response coupled only to baryons. The simple version of the idea failed, and we say so plainly.
A single coherence variable orders systems by their gravitational behavior.
The organizing quantity is a dimensionless coherence parameter built from local density and velocity dispersion:
High C corresponds to a coherent regime (galaxies, MOND-like phenomenology); low C corresponds to a chaotic regime (clusters, CDM-like phenomenology); galaxy groups straddle the boundary.
The galactic acceleration law that emerged repeatedly from the coherence picture is the Bose-mechanism radial acceleration relation:
The acceleration scale a₀ ties to cosmological structure rather than appearing as a free parameter.
A succession of attempts, most rejected, leaving a smaller surviving structure.
The starting premise was deliberately broad: that the vacuum responds dynamically to matter and curvature, and that this response might account for the gravitational anomalies we attribute to dark matter and dark energy. The early ideas explored that premise in many directions — vacuum response, vacuum phase-locking, nonlocal gravity coupling, and assorted attempts to derive modified-gravity behavior from vacuum coherence directly. The SPARC/RAR structure emerged repeatedly from these efforts; a coherence/transport operator framework consistently improved galaxy fits.
Bullet-Cluster-type systems then broke purely baryonic-response gravity. That failure was decisive. The work pivoted toward superfluid / coherent dark-sector ideas, then toward modular-horizon interpretations. By the time the dust settled, the original ambition — replacing dark matter outright — had given way to a narrower claim: vacuum coherence appears to govern galactic-scale gravitational phenomenology, but the cluster-scale story is a separate problem that the simple formulation does not solve.
An exploratory direction; no claim of closure.
The current research direction asks whether galaxy-scale vacuum coherence survives cluster collisions as interacting phase structures — galaxies modeled as coherent vortices, cluster dynamics modeled as interacting vortex fields, with the question being whether multi-domain phase interactions can generate large-scale persistent curvature structures that do not track the shocked gas. The mathematical intuition resembles superfluid turbulence, nonlinear phase-field dynamics, and collective emergent flow systems.
This is the central open research direction of the dark matter program. It is not a result. The framework no longer claims to replace dark matter outright — that question is open. The integration with the cosmological constant program below is a longer-term possibility.
The Gradient-Activated Pressure (GAP) paper, v40 from April 2026, documents the first-generation formulation of Vacuum Gravity Theory: a Ξ scalar field, the 4π³ Euclidean bridge, and the master action from which the galactic-scale results were derived. It is preserved here as a record of the original framework. The current research direction supersedes it where the cluster-merger physics is concerned.
Download GAP v40 (PDF, archival)A paper for the current vortex / multi-domain direction is in preparation.
Critique especially welcome. We have stated the failure plainly because we want it engaged with — mathematical objections, alternative reformulations, and pointers to relevant prior work are all useful.