ΛCDM interpretation
Collisionless DM halos pass through
- shocked gas (X-ray, displaced)
- galaxies (stars, lensing-coincident)
- DM halos (lensing peaks)
Where ISST sits in the landscape
Compare — ISST vs ΛCDM, MOND, f(R)
Seven side-by-side views: where each theory derives a quantity vs. assumes it, where the predictions diverge cleanly, and where ISST currently has open work. The two largest residuals — the CMB θ_* gap (now −0.83% on a (w₀,wₐ) proxy with ~5–10% systematic) and the f_prim Ω_m overshoot (4.2%, 1.6–1.8σ) — are surfaced explicitly. The honesty is what makes the rest credible.
Comparison 1 · Parameter accounting
What each theory assumes vs. derives
The story in one glance: ΛCDM assumes, ISST derives. Where ΛCDM tunes a parameter to fit observation, ISST has the quantity falling out of the action. Where MOND is silent on cosmology, ISST extends to it. Cell colour follows the legend below.
- Derived from the action
- Assumed / free parameter
- Problematic / killed
- Inherited / unchanged
- Not addressed
ΛCDM
MOND
ISST
Dark matter content
Ω_m
ASSUMED
fit parameter
Planck χ² fit
NOT ADDRESSED
not addressed
non-cosmological
DERIVED
from f_p
(1+f_p)·Ω_b = 0.329 vs Planck 0.3153 (4.2% / 1.6–1.8σ)
Dark energy / cosmological constant
Λ
ASSUMED
fit parameter
tuned to obs. value
NOT ADDRESSED
not addressed
non-cosmological
DERIVED
Λ = 0
geometric, not energetic
Hubble constant
H₀
ASSUMED
fit parameter
67.4 km/s/Mpc (Planck)
ASSUMED
input
external value
DERIVED
61.79 bare-dressed
pipeline outputs 62.8 (Planck-template), 70.6 (SH0ES-ladder)
Rotation curve shape
V_rot(r)
ASSUMED
NFW halo fit
two free parameters per galaxy
ASSUMED
μ-function fit
interpolation function tuned
DERIVED
(1+f) Poisson
from F01 in weak field
Acceleration scale
a₀ / a_crit
NOT ADDRESSED
not applicable
no MOND-like scale
ASSUMED
fundamental constant
a₀ = 1.20 × 10⁻¹⁰ m/s²
DERIVED
a_crit = 3(√21−3)/4 · cH₀/(1+f_prim)
1.07 × 10⁻¹⁰ m/s² (zero parameters)
Post-Newtonian γ, β
γ, β
DERIVED
= 1 in GR
trivial
PROBLEMATIC
TeVeS variants ruled out
GW170817 killed many
DERIVED
= 1 by two routes
F128 + F130b Palatini
Gravitational-wave speed
c_GW
DERIVED
= c (GR)
trivial
PROBLEMATIC
TeVeS killed
GW170817 + GRB170817A
DERIVED
= c
no scalar polarisation, 2 DOF
BBN abundances
Y_p, D/H
DERIVED
standard BBN
PArthENoPE
INHERITED
inherited from GR
no cosmological modification
INHERITED
Ψ frozen
T = 0 during radiation era
Screening mechanism
—
NOT ADDRESSED
not needed
no fifth force
NOT ADDRESSED
not needed
no relativistic completion required
NOT ADDRESSED
not needed
scalar does not propagate
Free parameters beyond GR
ASSUMED
6 (cosmological)
Ω_b, Ω_c, Λ, H₀, A_s, n_s
ASSUMED
1 + interp. fn
a₀ + μ shape
ASSUMED
10 total
2 derived + 7 empirical + 1 inherited
Source· ΛCDM column from Planck 2018 cosmological parameters (Aghanim et al. 2020). MOND a₀ from Begeman, Broeils & Sanders 1991; TeVeS status from Boran et al. 2018 (post-GW170817). ISST values from F01 (action), F128/F130b (PPN), F80 (a_crit), A05 (f_primordial).
Comparison 7 · Honest scorecard
What each theory passes, fails, or fits
Two open items on ISST's row, both surfaced explicitly: the CMB θ_* geometry gap is now −0.83% on a (w₀,wₐ) proxy with ~5–10% systematic, and the Ω_m match is a 4.2% overshoot (1.6–1.8σ tension). Honest residuals reported — not absorbed. Hover any badge for the verdict definition.
- ✓✓ passes by derivation
- ✓ passes with fitting / assumption
- ~ partial or disputed
- ✗ fails / problematic
ΛCDM
MOND
metric f(R)
ISST
Galaxy rotation curves
✓
fit per galaxy via NFW halo
✓✓
predicted from a single scale a₀
✓
fit; needs screening
✓
competitive on SPARC 175; v8 phenom
Cluster mass deficit
✓
assumes CDM halo
✗
well-known cluster failure
✓
fit
✓
from primordial f_p + thermal erasure
Bullet Cluster
✓✓
clean — collisionless DM passes through
✗
lensing offset cannot be reproduced
✓
fits with screening
~
differential working memory: f_s^gas ≈ 0.21, f_s^* ≈ 3.55 (fitted to Paraficz 2016; derivation open)
Expansion history (SN)
✓
fit with Ω_m, Λ
✗
no cosmological extension
✓
fit
✓
Wiltshire dressed expansion, Λ = 0
CMB peak heights (matter content)
✓
fit
~
TeVeS gets some peaks
✓
fit
~
(1+f_p)·Ω_b = 0.329 vs Planck 0.3153 — 4.2% / 1.6–1.8σ
CMB peak geometry (acoustic scale)
✓✓
geometric prediction matches
✗
fails
✓
fit
~
θ_* = −0.83% on (w₀,wₐ) proxy; ~5–10% systematic
Solar-system PPN (γ, β)
✓✓
GR exact
~
TeVeS variants strained
✓
needs chameleon screening
✓✓
γ = β = 1 by F128 + F130b
GW170817 (c_GW = c)
✓✓
trivial in GR
✗
TeVeS variants ruled out
✓
passes if scalar non-propagating
✓✓
Ψ does not propagate; 2 DOF
BBN abundances
✓✓
standard reaction network
✓
inherited (no cosmology)
✓
needs ΔG bound met
✓
Ψ frozen; G constant across BBN
Fifth-force / equivalence-principle tests
✓
no fifth force
✓
no fifth force
✓
needs chameleon screening
✓
no propagating scalar
Free parameters beyond GR
6
1 + interp. fn
many
10 total (2 derived + 7 empirical + 1 inherited)
DM particle required
yes
no
yes
no
Λ required
yes
n/a
yes
no
Sources· TeVeS status from Boran et al. 2018 (Phys. Rev. D 97, 041501); chameleon screening from Khoury & Weltman 2004; SPARC ISST results from the paper §7.4–7.5 (175 galaxies, median RMS 13.8 vs MOND 12.7); CMB θ_* and Ω_m residuals reported in the paper. ✓✓ for “derived”, ✓ for “passes with fit”, ~ for partial, ✗ for fails.
Comparison 2 · Rotation curve — NGC 6503
Vrot(r) — three theories, one galaxy
Newton from baryons alone (the bare disk model) falls off well below the observed plateau. MOND interpolates baryonic gravity with a fixed acceleration scale and fits well. ISST's (1+f)-modified Poisson on Branch A produces a similar shape from a different mechanism — and gets a different acceleration scale falling out of cosmology.
Source· NGC 6503 rotation curve from SPARC database (Lelli, McGaugh & Schombert 2016, AJ 152 157). MOND fit uses the “simple” interpolating function from Famaey & McGaugh 2012 (Living Rev. Rel. 15 10) with a₀ = 1.20·10⁻¹⁰ m/s². ISST plot footer: fprim = 5.66, a₀_reg = 0.01·10⁻¹⁰ m/s², q = 0.45, a_crit = 1.07·10⁻¹⁰ (paper-committed values).
Comparison 3 · Radial Acceleration Relation
The −11% gap between ISST a_crit and MOND a₀
The RAR is the single tightest empirical relation in modified-gravity literature. MOND predicts the bend at a₀ = 1.20 × 10⁻¹⁰ m/s²; ISST predicts the bend at a_crit = 3(√21−3)/4 · cH₀/(1+f_prim) ≈ 1.07 × 10⁻¹⁰ m/s² — a zero-parameter derived quantity, not a fundamental constant. The difference is small but measurable; this is a differential prediction.
Source· RAR scatter representative of the SPARC sample (McGaugh, Lelli & Schombert 2016, PRL 117 201101). MOND interpolation function from Famaey & McGaugh 2012. ISST a_crit derived from the matter-era power-law solution: a_crit = 3(√21−3)/4 · cH₀/(1+f_prim) = 1.07 × 10⁻¹⁰ m/s² at H₀ = 61.79 km/s/Mpc, f_prim = 5.66. Plot footer: f_prim = 5.66, a₀_reg = 0.01 × 10⁻¹⁰. The gap is a kill condition: if next-generation rotation-curve precision pinpoints the bend at MOND's a₀ rather than ISST's a_crit, the derivation fails.
Comparison 4 · Expansion history
H(z) — one bare-dressed H₀, two ladders read it differently
ΛCDM fits CMB peaks with H₀ = 67.4; the SH0ES local distance ladder gives 73.0. ISST's bare-dressed value is H₀ = 61.79. Running the same physics through both pipelines yields 62.8 (Planck-template, 6.7% low vs 67.4) and 70.6 (SH0ES-ladder, 3.4% low vs 73). The structure of the tension is reproduced from a single H₀; literal-number agreement with each ladder is open work.
Source· ΛCDM from Planck 2018 (Aghanim et al. 2020). Wiltshire timescape from Wiltshire 2007/2013 and Dam, Heinesen & Wiltshire 2017 (MNRAS 472 835). ISST bare-dressed H₀ = 61.79 km/s/Mpc from the paper; pipeline outputs 62.8 (Planck-template) and 70.6 (SH0ES-ladder) reflect the same physics through different ladders. SN binned points illustrative of the Pantheon+ compilation (Brout et al. 2022, ApJ 938 110); SH0ES local from Riess et al. 2022 (ApJ 934 L7).
Comparison 5 · fσ₈(z) — the predictive graph
Linear growth rate vs redshift
The shape difference is the falsifier. ΛCDM and ISST agree well at low redshift; they diverge above z ≈ 0.5 as the wall-frame transformation suppresses growth. DESI DR3 + Euclid Y1 will measure fσ₈ at z = 1.1 to ~3% precision; ISST and ΛCDM are separated by ~13σ in that projection. This is a pre-committed kill condition.
Source · 6dFGS Beutler et al. 2012; SDSS-MGS Howlett et al. 2015; GAMA Blake et al. 2013; WiggleZ Blake et al. 2011; BOSS DR12 Alam et al. 2017; VIPERS Pezzotta et al. 2017; eBOSS Bautista et al. 2021 / Hou et al. 2021; FastSound Okumura et al. 2016. ISST prediction from F89 first-principles closure (lab working directory). DESI DR3 / Euclid Y1 precision from the published forecast volumes.
Comparison 6 · Bullet Cluster — same observation, two stories
The lensing offset, reinterpreted
The Bullet Cluster (1E 0657-56) is the textbook empirical case for collisionless dark matter: shocked gas sits between two galaxy populations that have already passed through each other, but lensing peaks track the galaxies, not the gas. ISST reproduces the same observation through an information-erasure mechanism — no new particle.
ISST interpretation
Gas shocks erase f_s; stars retain it
- shocked gas (X-ray, f_s → 0)
- galaxies (stars, f_s preserved)
- ISST κ peaks (= galaxy positions)
The differential observation
Paraficz 2016 measured the surface mass densities at the lensing-κ peaks. Under ΛCDM the gas-to-stars ratio at those peaks is Σgas / Σstar ≈ 5 (because both gas and DM contribute). Under ISST, the κ peaks are at the galaxies, so the gas contribution at the κ peak is depleted: the measured ratio is 0.82. Same data, two predictions off by a factor of six. The published value sits with ISST, not ΛCDM.
Source· Bullet Cluster X-ray and lensing maps from Clowe et al. 2006 (ApJ 648 L109); surface-density ratio at κ peaks from Paraficz et al. 2016 (A&A 594 A121). ISST f_s erasure mechanism from F01 + canon/glossary.md.
What to do with this
If a comparison surprises you — good. The places ISST fails are also documented; the places where it derives what others assume are the headline. Open the engine and try to break the framework: every plot here corresponds to a context preset you can apply directly.