Work in progress · 2026
One postulate. Zero free parameters. Gravity, particle physics, and cosmology derived from Planck-scale discrete structure.
Landmark predictions — zero free parameters
| Result | Predicted | Observed | Status |
|---|---|---|---|
| Cosmological constant \(\Lambda\) | \(1.13\times10^{-52}\ \text{m}^{-2}\) | \((1.088\pm0.030)\times10^{-52}\ \text{m}^{-2}\) | within 1.4σ (3.7%) |
| Higgs boson mass \(m_H\) | \(124.8\pm2.4\ \text{GeV}\) | \(125.25\pm0.17\ \text{GeV}\) | 0.19σ |
| Area quantum \(\Delta A\) | \(4\ln(442)\,\ell_P^2 \approx 24.37\,\ell_P^2\) | LQG analogue | Derived |
| Barbero–Immirzi analogue \(\gamma_{\rm DEG}\) | \(\approx 2.24\) | From \(g = 442\) | Derived |
| Page curve \(S_{\rm rad}(k)\) | \(\min(k,\,N{-}k)\ln 442\) | Exact from finite-dim \(\mathcal{H}\) | Exact (leading order) |
| WdW unitarity | Exact | Kinematic from finite-dim \(\mathcal{H}\) | Exact |
| Born rule | \(P = g^k/g_{\rm total}\) | No collapse postulate required | Semi-derived |
Framework results — derived, load-bearing
Falsifiable predictions
| Observable | Prediction | Experiment | Timeline | Falsifier |
|---|---|---|---|---|
| Already confirmed | ||||
| GW speed \(c_{\rm GW}\) | \(= c\) exactly | GW170817 | ✓ confirmed | — |
| Ongoing | ||||
| No WIMP signal | Zero direct detection | LZ / XENONnT | ongoing | WIMP detection |
| CPT-odd LV \(\eta_1\) | \(= 0\) [approximate] | Fermi-LAT / CTA | ongoing | Any CPT-odd MDR detection |
| MOND acceleration \(a_0^{\rm DEG}\) | \(8.8\times10^{-11}\ \text{m/s}^2\) | SPARC / Vera Rubin | ongoing | 27% below observed — inconsistent with discrete spacing |
| Structure growth \(\sigma_8\) | \(0.78\pm0.02\) | Weak lensing surveys | ongoing | — |
| 2–5 years | ||||
| Dark energy \(w\) | \(= -1\) exactly | DESI / Euclid | 2–5 yr | Any \(5\sigma\) \(w\neq-1\) detection |
| Power spectrum \(P(k)\) | Two-scale suppression \(k\sim0.4\) and \(90\,h/\text{Mpc}\) | DESI / Euclid | 2–5 yr | Suppression at neither scale |
| 3–10 years | ||||
| Normal neutrino ordering | \(m_{\nu_1}\sim10^{-5}\ \text{eV}\) | JUNO | 3–5 yr | Inverted ordering confirmed |
| Neutron EDM \(d_n\) | \(2\times10^{-53}\text{–}6\times10^{-40}\ e{\cdot}\text{cm}\) | n2EDM@PSI | ~2026 | Signal \(>10^{-26}\ e{\cdot}\text{cm}\) |
| Proton decay \(\tau_p\) | \(\sim10^{33\text{–}34}\ \text{yr}\) | Hyper-Kamiokande | 5–10 yr | \(\tau_p > 10^{35}\ \text{yr}\) |
| 2030s–2037 | ||||
| Tensor-to-scalar ratio \(r\) | \(0.00452\pm0.002\) [semi-derived] | CMB-S4 / LiteBIRD | ~2032 | \(r > 0.01\) |
| Non-Gaussianity \(f_{\rm NL}\) \(^\dagger\) | \(\sim0.008\) (null) [derived] | CMB-S4 | ~2032 | \(f_{\rm NL} > 1\) at \(2\sigma\) |
| Env. Tully–Fisher variation | \(\lesssim10\%\) [conditional] | Vera Rubin / LSST | ~2030–35 | Zero variation at \(5\sigma\) |
| Triple Higgs coupling \(\kappa_\lambda\) | \(-1.449\pm0.17\) | HL-LHC | ~2035 | SM value \(\kappa_\lambda=1\) decisively excluded |
| Di-Higgs cross-section \(\sigma_{HH}\) | \(57.5\pm10\ \text{fb}\ (1.85\times\text{SM})\) | HL-LHC | ~2035 | \(\sigma < 40\ \text{fb}\) at \(5\sigma\) |
| Dark matter X-ray line | \(3.5\text{–}5\ \text{keV}\ (\nu_{R_1},\ m_s\sim7\text{–}10\ \text{keV})\) | ATHENA | ~2035 | Non-detection in viable window |
| LISA breathing mode \(^\dagger\) | \(h_{\rm br}/h_{\rm tensor}\sim6\times10^{-14}\) | LISA | ~2037 | Polarisation above \(10^{-3}\) |
| EMRI phase shift \(^\dagger\) | \(\Delta\Phi\sim10^{-82}\ \text{rad (null)}\) | LISA | ~2037 | Phase anomaly at LISA sensitivity |
| Long-term | ||||
| CMB \(\mu\)-distortion | \(\mu\sim10^{-5}\) | PIXIE / Voyage 2050 | 15–20 yr | \(\mu < 10^{-6}\) |
| Di-Higgs at 100 TeV | \(2267\pm400\ \text{fb}\) | FCC-hh | ~2040+ | — |
| Eff. Brans–Dicke \(\omega_{\rm BD}^{\rm eff}\) | \(\approx 4\times10^{11}\) | — | derived | Exceeds Cassini bound by \(\sim10^7\) |
| Casimir deviation | Deviation from \(1/d^4\) at \(d < a\) | CANNEX | long-term | No deviation at \(d\sim0.74\ \mu\text{m}\) |
\(^\dagger\) Null prediction: DEG predicts signal below experimental threshold. Detection above threshold would falsify.
Known tension
Higgs coupling \(\kappa_V = 0.432\)
Currently \(14.2\sigma\) from the LHC measurement at tree level. Non-perturbative DGMLY enhancement raises the analytical ceiling to \(\kappa_V = 0.797\) (\(5.1\sigma\)); no analytical method reaches \(\kappa_V > 0.920\). Reaching \(2\sigma\) compatibility requires \(m_{a_1}/m_\rho \geq 3.80\), a factor of \(2.2\times\) the large-\(N_c\) expectation. Resolution requires DEG-L Group C lattice computation of the \(\mathrm{SU}(3)_{\rm fam}\) V−A spectral function.
Systematic uncertainty
Cosmological constant factor-2
\(\Lambda_{\rm pred}\) carries a factor-2 systematic from non-perturbative \(\xi_{\rm UV}\) matching. Sub-factor-2 precision requires DEG-L-1 lattice ensemble. The zero-parameter central value is unaffected.
Partially derived
Baryon asymmetry \(\eta_B\)
Compatible with observation but not precisely derived. CP phase magnitudes are consistent within range; a fully quantitative derivation requires completing the leptogenesis calculation with fixed \(\varphi_{\rm DEG}\).
Not yet derived
Galaxy cluster profiles at large \(r\)
The MOND mechanism provides partial screening only. Quantitative cluster mass profiles at large radii are not yet derived. DEG predicts no dark matter halos; the cluster regime is the hardest test of this sector.
Outside current framework
Spectral index \(n_s\)
The DEG quantum epoch gives \(n_s = 4\) — a proof that spacetime atoms were not yet formed when the primordial spectrum was generated. The observed \(n_s \approx 0.963\) is a fossil of the pre-geometric phase \(\tilde{G} \supset \mathrm{SU}(21)\times\mathrm{U}(1)\), transferred unchanged through condensation. Eight internal mechanisms exhausted. Identifying \(\tilde{G}\) is the natural next extension of the programme.
Resolution path identified
DEG-L lattice programme
Four ensemble specifications (E1–E4) are complete. Three observable groups: topology (\(K_{\rm fam}\)), Higgs floor, V−A spectral function (\(\kappa_V\)). Estimated ~\(10^5\) GPU-hours. No paper is analytically blocked by DEG-L; it sharpens existing results.
DEG posits that spacetime is a statistical aggregate of \(N\) discrete Planck-scale atoms, each characterised by a size parameter \(a_n\) and an internal Hilbert space of dimension \(g = 442\). The dynamics is governed by a single Hamiltonian constraint — no background metric, no continuous fields at the fundamental level.
From this foundation, the programme derives without fitting any parameter to observation: macroscopic time and the thermodynamic arrow; Newton's law and the Einstein field equations; the observed cosmological constant; galaxy rotation curves via a MOND-like mechanism; the Standard Model gauge group and three generations; the Higgs boson mass; and the exact resolution of the black hole information paradox via a finite-dimensional Hilbert space.
What is not claimed. DEG is not a complete theory of quantum gravity. The derivations rest on statistical and thermodynamic assumptions whose full quantum justification remains open. DEG is a theory of the post-condensation universe — describing cosmic history from spacetime atom formation (~\(T_{\rm reheat}\sim10^{18}\) GeV) through today, approximately 97% of cosmic history in log energy scale. The pre-geometric epoch that preceded condensation, and whose near-conformal dynamics generated the observed CMB tilt, lies outside the single-postulate framework by construction — in the same sense QCD does not derive the electroweak gauge group. That boundary is identified and named; the programme is offered as a coherent, falsifiable research direction within it.
Research pipeline — papers in preparation
This page is updated as each paper becomes available.
Like loop quantum gravity and causal set theory, DEG takes discreteness as fundamental. It differs in using a statistical mechanics approach: gravity and time emerge thermodynamically, not through geometric quantisation.
The cosmological constant result is, to our knowledge, the first zero-parameter derivation of the observed \(\Lambda\) from any discrete spacetime programme. The key mechanism: the UV cutoff is the micrometre-scale atom spacing \(a\approx0.74\,\mu\text{m}\), not the Planck length — suppressing vacuum energy by \((a/\ell_P)^3\sim10^{86}\).
The Higgs mass prediction is notable for its origin: \(m_H\) is derived from CP-violating observables (\(\delta_{\rm CKM}\) and \(\eta_B\)) through a single internal parameter \(\varphi_{\rm DEG}\) that simultaneously satisfies seven independent constraints across flavour physics, leptogenesis, and the Higgs sector.
The programme is falsifiable at multiple near-term experiments. The most decisive single test is \(w = -1\): any \(5\sigma\) detection of \(w\neq-1\) by DESI or Euclid rules out the entire dark energy sector. DESI DR2 (2025) currently shows a \(3.1\sigma\) preference for dynamical dark energy in combined analyses — suggestive but below the falsification threshold, and sensitive to the choice of supernova compilation.
Domain of validity. DEG has a clean jurisdiction: the post-condensation universe. The CMB spectral index \(n_s \approx 0.963\) is not a DEG prediction — it is a fossil of the pre-geometric phase that preceded spacetime atom formation, transferred unchanged through condensation. The DEG quantum epoch gives \(n_s = 4\), which is the correct result for fluctuations of the already-formed atom lattice, and simultaneously a proof that the atoms were not present earlier. The pre-geometric symmetry \(\tilde{G} \supset \mathrm{SU}(21)\times\mathrm{U}(1)\) whose breaking selects \(g = 442\) is the identified natural extension.
Matteo Pinna is a theoretical physicist working independently on quantum gravity and emergent spacetime. His interest in emergent gravity began during his thesis work in 2018, shaped by a conviction that the foundations of physics should admit a simple, parameter-free description — and a specific dissatisfaction with the treatment of time in general relativity.
The starting point was a refusal to accept time as a curved fourth dimension behaving differently from the other three. If space is emergent, time should be too — and the arrow of time, rather than being imposed by initial conditions, should follow from the statistics of whatever is fundamental. DEG is the formalisation of that programme, developed over several years alongside a career in technology.
He is based in Madrid.
Further papers are in preparation. This page will be updated as each becomes available.
Poster material will be made available here via Zenodo once uploaded.
If you work in quantum gravity, emergent spacetime, or related areas and find this programme of interest, I would welcome correspondence — critical feedback especially.
matteo@deg-gravity.com
I am an independent researcher based in Madrid. Collaboration enquiries and comments from researchers with relevant expertise are very welcome.
The papers above contain full derivations, explicit uncertainty budgets, and complete lists of open problems. Nothing is behind a paywall or submission requirement.
All preprints are available directly on this page as PDF. They represent work in progress and will be updated prior to submission.
The complete research programme — all derivations, results, and open problems — is consolidated in a single citable document published on Zenodo: doi.org/10.5281/zenodo.20434554
If you are a physicist encountering DEG for the first time and would like to discuss the approach, its foundations, or its limitations, please feel free to write. I am also happy to share derivation notes on specific points not fully developed in the papers.