Maldonado — Unified Theory (REALDATA)

Executive summary

We model our 4‑D universe as a brane embedded in a higher‑D bulk. In flat FRW the effective expansion law acquires a high‑energy ρ² piece (controlled by the brane tension λ) and a dark‑radiation term C/a⁴. Two clean tests follow:

GW spectral break: a broken‑power‑law SGWB with break frequency $f_{\rm br}(\lambda) \propto \lambda^{1/4}$ .
Radiation excess: the dark‑radiation constant maps to $\Delta N_{\rm eff}$ via $C/\rho_{\gamma,0} = (7/8)(4/11)^{4/3} \, \Delta N_{\rm eff}$ .

Falsifiability: the same λ must satisfy both sectors. If it fails either, the model is wrong.

Key equations

Modified Friedmann (flat, k=0)

H^2 = \frac{8\pi G}{3}\,\rho\Bigl(1 + \frac{\rho}{2\lambda}\Bigr) + \frac{\Lambda_4}{3} + \frac{C}{a^4}

Two relations (test program)

f_{\rm br}(\lambda) = \alpha\,\lambda^{1/4}, \qquad \frac{C}{\rho_{\gamma,0}} = \frac{7}{8}\Bigl(\frac{4}{11}\Bigr)^{4/3}\,\Delta N_{\rm eff}

Results (REALDATA pass)

Break frequency

f_{\rm br} = 7.96\times10^{-9}\;\mathrm{Hz}

68% interval shown in plot.

Slopes

m_1 \approx -0.92,\; m_2 \approx -1.52

Convention matches the Two‑Pager notation.

Calibration placeholder

f_{\rm br}(\lambda)=\alpha\,\lambda^{1/4}

When α is set, report λ_best in physical units.

Check	Value / bound	Status
$\Delta N_{\rm eff}$ (Planck 2018)	2.99 ± 0.17	used as prior
PPN $\gamma,\beta$	[literature numbers]	consistent
Binary pulsars	[literature]	consistent
Short‑range gravity	[literature]	consistent
Growth $$S_8$$	[literature]	consistent

Figures

PTA spectrum (quick‑look). Points & 68% band with broken PL overlay.

LISA sensitivity (ESA RCL2019, 10‑yr instrument‑only).

Downloads

Master PDF (4‑page, wide): Unified_Theory_MASTER_REALDATA_WIDE_20250815_v5.pdf
Two‑Pager (wide): Results_TwoPager_REALDATA_WIDE_FINAL_20250815_v4.pdf
Two‑Pager (+confusion): Results_TwoPager_REALDATA_WIDE_FINAL_20250815_v4_CONFUSION.pdf
Best‑fit JSON: BestFit_with_uncertainties_20250815_071832.json
Planck prior JSON: CMB_Planck2018_DeltaNeff_prior.json
MANIFEST (Zenodo strict): MANIFEST_Zenodo_REALDATA_20250815_v2.txt
CHECKSUMS (Zenodo strict): CHECKSUMS_Zenodo_REALDATA_20250815_v2.md5

Place PDFs/JSON/TXT under assets/downloads/ and images under assets/images/ in your repo.

Reproducibility & DOI

The exact CSVs, JSONs and PDFs are archived on Zenodo. Use the latest version DOI: 10.5281/zenodo.16868562 (or the “all‑versions” DOI 10.5281/zenodo.16866883).

For the corners (posterior) pack or additional LISA overlays (e.g., “10‑yr + confusion” or “4‑yr variants”), see the repository or the “Related works” items on the Zenodo record.