Figures & Media

Numerical verification that f_NL = −35/8 is identical across three bounce mechanisms: pure dust contraction, quintom bounce (H = Υt), and asymmetric Papanikolaou bounce (w: 0→1/3). The bispectrum is determined by contraction-phase dynamics, not the bounce UV completion.

Negative f_NL from the matter bounce naturally suppresses PBH overproduction. Left: PBH abundance f_PBH vs perturbation amplitude σ for f_NL = 0, −35/8, +4.375, +10. Right: the non-Gaussian PDF tail cutoff. The matter bounce value keeps f_PBH ∈ [10⁻³, 1] without fine-tuning — a unique advantage over inflationary PBH models.

The matter-bounce induced GW spectrum has universal f² infrared scaling (γ = 3), consistent with NANOGrav 15-year data (γ = 3.2 ± 0.6) at 0.33σ. SMBH binary mergers predict γ = 13/3 (1.9σ tension). The bounce prediction requires no free parameters.

Template fit of NANOGrav 15yr free-spectrum data. Matter bounce (γ=3.0) preferred 302:1 over SMBH mergers (γ=13/3) and 81,000:1 over cosmic strings (γ=5/3). 4-panel: h_c(f), residuals, Ω_GW, comparison table. Caveat: synthetic data from published power-law, not raw free-spectrum posteriors.

Converged MCMC posterior (50,880 samples, R-1=0.009). Left: w₀–w_a contour with ΛCDM and DESI DR2 points. Center: w(z) reconstruction showing crossing at z≈0.6. Right: summary statistics. P(quintom-B) = 98.0%.

First 500K spectra from the 45-column enhanced DESI DR1 catalog. Key finding: galaxies are 19× more likely to be anomalous than QSOs (0.76% vs 0.04%). Score vs S/N shows no correlation (anomalies are NOT noise artifacts). Anomalies peak at z∼0.3–0.5.

The complete bispectrum shape \(S(k_1,k_2,k_3)\) for matter contraction, showing squeezed limit \(f_\mathrm{NL} = -35/8\) and equilateral/folded special cases.

Detection significance for \(f_\mathrm{NL} = -35/8\) across survey configurations, with GR marginalization bands. SPHEREx: ~5.5\(\sigma\) (template-corrected); MegaMapper: ~7.5\(\sigma\).

How detection significance depends on the minimum measurable wavenumber, showing the critical role of ultra-large-scale modes.

Monte Carlo Bayes factor distributions: bounce vs inflation at various \(f_\mathrm{NL}\) values. Bayes factor ~8-17 vs multifield competitors (prior-dependent).

Parameter space comparison showing why negative \(\mathcal{O}(1)\) \(f_\mathrm{NL}\) is natural for bounce but requires fine-tuning for inflation.

Matter-bounce \(B_\mathrm{NL}\) vs local template across triangle configurations. Left: squeezed series showing convergence to \(-35/8\). Right: isosceles series showing 63% variation from folded (\(-2.25\)) to equilateral (\(-3.98\)). The local template is constant at \(-35/8\) for all configurations — the shaded area represents signal lost by a local estimator.

Amplitude recovery factor \(r\) across 10 physically motivated weighting schemes, using the physics-derived full-commutator polynomial (6,2,−18,10,−66,18). With the true polynomial: CMB Fisher r = 0.90, LSS/SDB r = 0.85, giving r ≈ 0.85–0.90. Mismatch is intrinsic to the bounce shape. Gray bars show adversarial extreme cuts.

Left: Detection significance with and without template mismatch correction (canonical \(f_\mathrm{NL} = -35/8\)). SPHEREx drops from \(6.2\sigma\) naive to \(5.5\sigma\) corrected. Right: Normalization sensitivity — if \(-35/16\) is correct, SPHEREx drops further to \(2.7\sigma\). Template correction matters more for the MegaMapper SDB channel.

Matter-bounce \(B_\mathrm{NL}\) shape: physics-derived polynomial (6,2,−18,10,−66,18) vs 3-benchmark fit (2,7,3,−12,−69,19). Left: isosceles series showing the true polynomial stays closer to the local template at intermediate configurations. Right: squeezed series showing both converge to \(-35/8\). The physics-derived polynomial gives a less severe template mismatch (\(r \approx 0.85\text{--}0.90\) vs \(r \approx 0.84\)).

Cosmic birefringence \(\beta\) measured from Planck SMICA using NaMaster with B-mode purification at increasing resolution. NSIDE=1024 (\(\beta = 0.19 \pm 0.03°\)) is the lead result. At NSIDE=2048, \(\beta\) drops to \(0.07 \pm 0.02°\), suggesting high-\(\ell\) contamination or noise. Green circle marks the preferred NSIDE=1024 result. Blue band shows the published Planck+ACT measurement. Red dashed line is our ALP prediction.

Detection significance for \(f_\mathrm{NL} = -35/8\) using the physics-derived polynomial (\(r = 0.88\)). Template correction reduces SPHEREx from \(6.2\sigma\) naive to \(\sim5.5\sigma\). MegaMapper drops from \(8.8\sigma\) to \(\sim7.7\sigma\). Both remain well above the \(5\sigma\) discovery threshold.

Cosmic birefringence angle \(\beta\) compared across multiple spin-torsion model variants and competing frameworks, showing the predicted signal range.

Updated corner plot from the v2 analysis with refined parameter constraints and additional dataset combinations.

Shows the derivation chain from Planck scale through one-loop parity-odd operator, inflationary suppression, to observed dark energy scale \(\rho_\Lambda \approx (2.3\;\mathrm{meV})^4\).

Dipole amplitude across SDSS DR7, Pan-STARRS, HST Deep, and Longo (2011) with hierarchical Bayesian fit. Status: contested anomaly.

Shows spin-torsion model position between Planck and SH0ES/KiDS measurements. Note: tension reduction was disproved by independent MCMC. [Historical: tension reduction was later shown to be SH0ES-prior-driven]

\(H_0\) and \(\sigma_8/S_8\) measurements from 9+ probes with spin-torsion model position overlaid for direct comparison. [Historical: tension reduction was later shown to be SH0ES-prior-driven]

Luminosity and angular diameter distance deviations from \(\Lambda\)CDM at the ~2% level, showing observational signatures of geometric dark energy.

\(H(z)\) comparison showing the rotation contribution is negligibly small (< \(10^{-20}\)), confirming the model is expansion-equivalent to \(\Lambda\)CDM.

Log-scale fine-tuning: \(\Lambda\)CDM (\(10^{120}\)), Quintessence (\(10^{60}\)), \(f(R)\) (\(10^{40}\)), Spin-Torsion (\(10^5\)). Note: \(10^5\) is illustrative. [Note: 10⁵ figure is reparameterized, not solved]

Key experimental milestones for testing the spin-torsion model: LiteBIRD (early 2030s, JAXA JFY2032), CMB-S4 (2029), LSST (2030), and SPHEREx.

Combined detection significance projections across multiple observational probes, showing cumulative constraining power over the next decade.

Corner plot showing 2D posterior contours for all primary cosmological parameters from the full-tension MCMC analysis with 176,840 samples.

1D marginalized posterior distributions for key cosmological parameters including \(H_0\), \(\Omega_b h^2\), \(\Omega_c h^2\), and \(\Delta N_\mathrm{eff}\).

Posterior distribution for the dark radiation parameter \(\Delta N_\mathrm{eff}\), with the spin-torsion prediction overlaid. Consistent with zero within 1\(\sigma\).

Chain convergence traces and \(\hat{R}\) evolution across iterations, confirming \(\hat{R} - 1 < 0.005\) for all parameters.

Pearson correlation coefficients between all sampled cosmological parameters, revealing the degeneracy structure of the spin-torsion model.

ESS accumulation across chain iterations, demonstrating sufficient independent samples for reliable posterior estimation.

\(H_0\), \(\Delta N_\mathrm{eff}\), and \(S_8\) posteriors compared across frozen dataset combinations (Planck+BAO, Planck+BAO+SN, Full-Tension).

Posterior distributions from both frozen datasets, demonstrating that both are consistent with \(\Delta N_\mathrm{eff} = 0\) at high significance.

4-panel Monte Carlo analysis: vacuum scale distribution, \(N_\mathrm{tot}\) sensitivity, viable fraction of parameter space, and Spearman rank correlations.

Analysis of potential spectral features in the matter power spectrum that could distinguish spin-torsion cosmology from vanilla \(\Lambda\)CDM.

Full architecture of the BigBounce research program, mapping the relationships between theoretical foundations, observational tests, and publication milestones.