Gravity from the Ledger of the Euler Universe: Dark energy and dark matter as the two faces of de Sitter horizon entropy
Abstract
Version 2 of Gravity from the Ledger of the Euler Universe (Euler Cosmos series S15).
The paper reads the local zero-energy constraint of canonical gravity, H(x) = 0, as a theory of gravity. Taking the principle that only the imbalance of the ledger gravitates, and joining it to the two-part (area-law and volume-law) entropy of the de Sitter horizon, it derives a modified force law, g_obs² = g_N² + g_N a0, with interpolation μ(x) = (√(1+4x²) − 1)/2x. The law matches the observed radial acceleration relation to 0.057 dex with no fitted function, gives the baryonic Tully–Fisher relation, and returns to Newton inside the transition radius r_M = √(GM/a0) by finite-entropy screening. The acceleration scale tracks the horizon, a0 ∝ cH(z), read at cH/2π. The theorem that matter removes de Sitter entropy, δS = −2πML, is proved. The relativistic completion is aether–scalar–tensor gravity, with the aether supplied by the ledger's foliation.
Version 2 places this paper in the series as it now stands. Since version 1, Space as a Substance (S23) has given space a material body, a chiral superfluid glass, and reads galactic dark matter as the glass's cold condensate. This version keeps its modified gravity as one of two dark-matter branches of the series and sets it beside the condensate as a rival, with a table of the observations that separate them: the redshift track of a0, wide binaries in Gaia DR4, tidal dwarf galaxies, the form of the radial acceleration relation, and cluster collisions. The glass settles part of the paper's open question. Its rigidity cannot hold the entropy deficit as a static pull (the Bianchi identity fixes the field by its sources), so the force law, if real, needs the added scalar and aether fields of the relativistic completion.
Also in version 2: the corrected sign of the gravitational kinetic term in the Hamiltonian constraint; the glass calibration of S13 (H0 = 67.0 km/s/Mpc, Ω_N = 1.09), which narrows the gap between cH0/2π and the measured a0 from 26% to 16%; the w = −1 crossing at z = 0.78 retired as superseded; the a0(z) test recomputed (horizon prediction χ²/N = 1.9 against the raw MUSE-DARK points, constant a0 excluded at 27; after the molecular-gas correction the horizon and vacuum-amount readings fit about equally and a constant remains disfavoured); falsification and a0(z) figures redrawn at the new calibration; first-person language removed.
Related
- One Gravity, Many G's: Generalized Horizon Entropy and Gravitational Susceptibility
- How Much Geometry Does Horizon Entropy Determine? A Discourse on Entropy, Gravity, and Observable Quantities
- The Topological Transition of the Vacuum 0 → Û(π) + Î: Hamiltonian Foundation of the Zero-Energy Universe and Torsional Dynamics of the Horizon
- The Chauhan-Matergy (CM) Closed-Loop Universe Model: A Fluid-Dynamic Framework for Gravity, Dark Energy, and Cyclic Cosmology
- Horizon energy fluctuations beyond Einstein's gravity: Gauss-Bonnet, Lovelock and Quantum deformed frameworks
BibTeX
@misc{sanders2026gravity,
title = {{Gravity from the Ledger of the Euler Universe: Dark energy and dark matter as the two faces of de Sitter horizon entropy}},
author = {Nicholas Archer Sanders},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23573420},
url = {https://zenodo.org/records/23573420},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gravity from the Ledger of the Euler Universe: Dark energy and dark matter as the two faces of de Sitter horizon entropy
AU - Nicholas Archer Sanders
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23573420
UR - https://zenodo.org/records/23573420
AB - Version 2 of Gravity from the Ledger of the Euler Universe (Euler Cosmos series S15). The paper reads the local zero-energy constraint of canonical gravity, H(x) = 0, as a theory of gravity. Taking the principle that only the imbalance of the ledger gravitates, and joining it to the two-part (area-law and volume-law) entropy of the de Sitter horizon, it derives a modified force law, g_obs² = g_N² + g_N a0, with interpolation μ(x) = (√(1+4x²) − 1)/2x. The law matches the observed radial acceleration relation to 0.057 dex with no fitted function, gives the baryonic Tully–Fisher relation, and returns to Newton inside the transition radius r_M = √(GM/a0) by finite-entropy screening. The acceleration scale tracks the horizon, a0 ∝ cH(z), read at cH/2π. The theorem that matter removes de Sitter entropy, δS = −2πML, is proved. The relativistic completion is aether–scalar–tensor gravity, with the aether supplied by the ledger's foliation. Version 2 places this paper in the series as it now stands. Since version 1, Space as a Substance (S23) has given space a material body, a chiral superfluid glass, and reads galactic dark matter as the glass's cold condensate. This version keeps its modified gravity as one of two dark-matter branches of the series and sets it beside the condensate as a rival, with a table of the observations that separate them: the redshift track of a0, wide binaries in Gaia DR4, tidal dwarf galaxies, the form of the radial acceleration relation, and cluster collisions. The glass settles part of the paper's open question. Its rigidity cannot hold the entropy deficit as a static pull (the Bianchi identity fixes the field by its sources), so the force law, if real, needs the added scalar and aether fields of the relativistic completion. Also in version 2: the corrected sign of the gravitational kinetic term in the Hamiltonian constraint; the glass calibration of S13 (H0 = 67.0 km/s/Mpc, Ω_N = 1.09), which narrows the gap between cH0/2π and the measured a0 from 26% to 16%; the w = −1 crossing at z = 0.78 retired as superseded; the a0(z) test recomputed (horizon prediction χ²/N = 1.9 against the raw MUSE-DARK points, constant a0 excluded at 27; after the molecular-gas correction the horizon and vacuum-amount readings fit about equally and a constant remains disfavoured); falsification and a0(z) figures redrawn at the new calibration; first-person language removed.
ER -