The Cosmic Acceleration Minimum from Inertia (CAMI): A One-Parameter Solution to Cosmological Tensions

The CAMI Constant: One invariant, two observables, zero new fields. This paper presents the first observationally testable prediction of a universal acceleration floor, called the Cosmic Acceleration Minimum via Inertia (CAMI), emerging from a spin–torsion coupling in Einstein–Cartan gravity. By mathematically deriving a residual acceleration term gσ=4πGc2 σ0,g_\sigma = \frac{4\pi G}{c^2}\,\sigma_0,gσ=c24πGσ0, we show that a conserved primordial spin density enforces a minimum gravitational acceleration, one that persists across all cosmic scales. This is not a free parameter or a fitted function: once σ0\sigma_0σ0 is fixed (e.g. from galaxy rotation curves), every CAMI prediction becomes locked in and falsifiable. We use this single scale to derive six closed-form predictions, and then test them, without tuning, against independent observational datasets. Six Observational Tests, One ConstantUsing public data from SPARC, DES-Y3, TDCOSMO, and Planck 2018, we compute exact predictions for: Radial–Acceleration Relation (RAR):CAMI explains the intrinsic scatter in 175 SPARC galaxies with stellar population uncertainty alone (RMS = 0.06 dex), with no dark halos. Dwarf Spheroidal Velocity Dispersions:A parameter-free relation σℓ2=π4gσR1/2\sigma_\ell^2 = \frac{\pi}{4}g_\sigma R_{1/2}σℓ2=4πgσR1/2 matches stellar kinematics across Local Group dwarfs. Weak Lensing Convergence:CAMI predicts a flat suppression in DES-Y3 κκ\kappa\kappaκκ spectra at large angular scales—∼1.5%, consistent with the observed amplitude tension. Strong-Lens Time Delays (TDCOSMO):A coherent Fermat shift from the CAMI potential predicts a −1.5%-1.5\%−1.5% bias in time-delay distances, reconciling SH0ES and Planck H0H_0H0 values. CMB Polarization ($E!B$ Leakage):The spin–torsion coupling induces a uniform rotation of CMB polarization: CAMI predicts α=0.32∘\alpha = 0.32^\circα=0.32∘, in agreement with Planck’s measured α=0.35∘±0.14∘\alpha = 0.35^\circ \pm 0.14^\circα=0.35∘±0.14∘. CMB Shear and Isotropy:CAMI’s torsional shear decays faster than vorticity, leaving large-angle CMB isotropy intact and below Planck bounds. Bayesian Joint Analysis We perform a full five-probe joint likelihood analysis using nested sampling via dynesty. The model contains one cosmological parameter (gσg_\sigmagσ) and five calibrated nuisance terms (e.g., shear calibration, M/LM/LM/L scatter, lens profile slope). Results: Best-fit torsion acceleration:log⁡10gσ=−10.89−0.05+0.06\log_{10} g_\sigma = -10.89^{+0.06}_{-0.05}log10gσ=−10.89−0.05+0.06→ γ=140.4−3.1+3.2\gamma = 140.4^{+3.2}_{-3.1}γ=140.4−3.1+3.2 Bayes factor vs. $\Lambda$CDM:Δln⁡Z=+16.5\Delta \ln\mathcal{Z} = +16.5ΔlnZ=+16.5 → 4.8σ preference All nuisance parameters remain within their priors. Robustness checks (e.g., prior expansion, multipole trimming, systematics variation) confirm model stability. Implications and Outlook CAMI offers a tightly constrained, testable alternative to the standard cosmological model, reproducing key large-scale structure and background features without dark matter profiles or additional scalar fields. It is falsifiable, minimal, and predictive. The next-generation missions, LiteBIRD, LSST, LISA, and additional TDCOSMO lenses, can decisively confirm or rule out CAMI’s predictions within the decade.