Inconclusive TestPaper P06

The Cosmology Grid Test Was Inconclusive (H0/S8)

The sweep found no configuration that met its resolution criterion, but it covered only part of its k range and used an H0 criterion no single H0 value can meet. It neither supports nor rules out the model.

Scientific Honesty: Publishing negative results prevents wasted effort and shows what approaches do NOT work.

Why Negative Results Matter

Science advances not just by discovering what works, but by rigorously documenting what does NOT work. Negative results prevent others from wasting time on dead ends and demonstrate scientific integrity.

What This Shows

  • - We tested the hypothesis and report the test's weaknesses
  • - We report results honestly, even when negative
  • - We save others time by showing this path fails
  • - We maintain scientific credibility

What Would Be Wrong

  • - Hiding failures and only showing successes
  • - Cherry-picking favorable results
  • - Overclaiming based on weak evidence
  • - Ignoring contradictory findings

Background: Cosmological Tensions

1

H0 Tension (Hubble Constant)

About 4.9-sigma discrepancy between the two values below

Early Universe (CMB - Planck)

H0 = 67.4 +/- 0.5 km/s/Mpc

Late Universe (Local - SH0ES)

H0 = 73.04 +/- 1.04 km/s/Mpc

This 5.6 km/s/Mpc difference (8%) suggests either new physics or systematic errors.

NASA: Webb & Hubble Confirm Expansion Rate Puzzle
2

S8 Tension (Matter Clustering)

2-3 sigma discrepancy in matter distribution

CMB Prediction (Planck)

S8 = 0.834 +/- 0.016

Weak Lensing Observed (KiDS)

S8 = 0.759 +/- 0.024

The universe appears less clumpy than predicted by early universe measurements.

eROSITA and S8 Tension (2024)

The Hypothesis We Tested

Hypothesis:

Modified Friedmann equations using Non-Newtonian Calculus with a single uniform k value can simultaneously resolve both H0 and S8 tensions by providing scale-dependent corrections.

Result: INCONCLUSIVE

The producer (simulations/cosmology_validation_moo.py) ran a grid sweep, not NSGA-II: only the first 200 grid configurations were evaluated, which covers k in [-0.50, -0.34] only (4 k values), and the 9 non-dominated points were kept. None met the "resolution" criterion, but that criterion (within 2 sigma of both SH0ES and Planck) cannot be met by a single H0: the two 2-sigma intervals do not overlap (the measurements are about 4.9 sigma apart). The full grid needs rerunning with an attainable criterion before this counts as evidence either way.

What the Stored Model Actually Does

Not a Uniform Scaling

The producer multiplies the classical expansion rate by H_meta / H_classical = 1 + k ln(1 + z), which already depends on redshift. For k = 0.1 the ratio is 1.0000 at z = 0 and 1.0693 at z = 1.

  • - An earlier version of this page argued that a constant k scales everything identically; for this model that is false
  • - The failed criterion comes from the test design (an unattainable H0 window), not from the shape of the correction
  • - So the run does not show that redshift- or scale-dependent physics is required

What a Real Test Would Need

Before this counts as evidence either way:

  • - The full grid (or an optimizer) over the whole k range
  • - An attainable criterion, for example a likelihood or tension-in-sigma threshold
  • - A physical mechanism for the k ln(1 + z) correction
  • - Independent evidence for that mechanism

The Evidence: MOO Results

A 200-configuration grid sweep (k, h, Omega_m), filtered to its 9 non-dominated points on chi-squared, fragility and |k|. Counts from results/cosmology_validation_moo.json (analysis block):

0/9

H0 Resolutions (criterion unattainable)

0/9

S8 Resolutions

-28%

Best Li7 "improvement" (worse)

The H0 shown for each point is 100h with h a free fit parameter; it is fitted, not predicted by k.

Interactive Evidence

The visualizer above shows the 9 non-dominated points of the grid sweep. None bridges both H0 and S8 gaps, but with only 4 k values sampled and an unattainable H0 criterion the test is inconclusive.

What This Teaches Us

Lesson 1: Test Your Hypotheses

We tested the cosmology idea instead of assuming it, and the first test is too narrow to be conclusive. Saying so is part of the result.

Lesson 2: Report All Results

Publishing this negative result is as important as publishing positive results. It shows the boundaries of where NNC applies and prevents publication bias.

Lesson 3: Understand Limitations

Read the model before arguing from it: the stored correction 1 + k ln(1 + z) already varies with redshift, so "a constant k scales everything the same" does not apply to it. No physics domain on this site has a validated positive result for NNC either.

Lesson 4: Honest Communication

We clearly state what does NOT work, not just what does. This builds trust and credibility in our positive results by showing we are willing to admit failures.

NNC: Where It Works vs Where It Fails

What Holds

  • Power-law diagnostics: L_BG[1/r] = -1 and D_BG[1/r] = exp(-1) for r > 0 (the field itself still diverges)
  • Toy benchmark only: the crack-tip and radiation percentages quoted elsewhere come from a synthetic distance-to-singularity toy, not physics

These are derivative identities on r > 0; they do not remove physical singularities.

Where NNC Fails

  • H0/S8 tensions: Not shown; the stored test is inconclusive
  • Quantum phase scan: 0 of 1000 configurations unitary (no k=0 point sampled)
  • Smooth diffusion: Nothing singular for the diagnostic to act on

Common pattern: no stored test supports a physics improvement.

Future Directions

Since this test is inconclusive, these are the productive directions:

  1. 1. Investigate k(z) profiles:

    Can redshift-dependent k values resolve tensions? What physical mechanism would justify this?

  2. 2. Focus on localized applications:

    Test NNC diagnostics on problems with a clear power-law structure before trying cosmology again.

  3. 3. Develop theoretical foundation:

    Derive k(scale) from first principles rather than fitting to data.

  4. 4. Document boundaries:

    Systematically map where NNC helps vs hurts to guide appropriate application.

Related Pages

Cosmological Tensions

Existence proofs for parameter fits (not resolutions) - what we CAN claim

CASCADE Toy Benchmark

Synthetic toy benchmark: distance to the centre of a 2-D objective, by profile (not physics results)

Lessons Learned

12 years of failures and what they taught us about honest science

What We CAN Verify

Spectral-gap boundary census and published bigeometric identities

References

[Planck 2020] Planck Collaboration, Aghanim, N., et al. (2020). Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics, 641, A6.

[Riess et al. 2022] Riess, A. G., et al. (2022). A Comprehensive Measurement of the Local Value of the Hubble Constant. The Astrophysical Journal Letters, 934, L7.

[KiDS 2021] Heymans, C., et al. (2021). KiDS-1000 Cosmology: Multi-probe weak gravitational lensing and spectroscopic galaxy clustering constraints. A&A, 646, A140.

[Grossman & Katz 1972] Grossman, M. & Katz, R. (1972). Non-Newtonian Calculus. Lee Press, Pigeon Cove, MA.

[Blank & Deb 2020] Blank, J. & Deb, K. (2020). Pymoo: Multi-Objective Optimization in Python. IEEE Access, 8, 89497-89509.