Nonminimally coupled exponential quintessence without the CMB: identifiability, Newton-constant normalisation and local-gravity consistency with DESI DR2 and Pantheon+

The study presents a background-level confrontation of the Jordan-frame scalar-tensor action F(φ) = M_*² + ξφ² with an exponential potential V(φ) = V₀ e-λφ/M_* against the DESI DR2 baryon acoustic oscillation (BAO) measurements and the Pantheon+ Type Ia supernova compilation (with validation on DES-SN5YR Dovekie), without incorporating cosmic microwave background (CMB) data. Key Features and Findings Cavendish Normalisation: Demonstrates that the bare scale M_* cannot be identified with the measured Planck mass; sampling the Cavendish-normalised matter fraction Ωₘ(N) = Γ₀ Ωₘ^* eliminates the sampler pathology and shows that the high-Ωₘ ridge found in bare parameterisations is a normalisation artefact. Shooting & Prior Attribution: Solves the V₀ shooting problem across eight decades using a multi-root scan. It classifies the uniform prior volume into histories without a self-consistent Hubble rate (36.7%), data exclusions (63.2%), and allowed histories (0.1%), with ghost and real-expansion walls never binding. Parameter Identifiability: Background distances constrain essentially a single combination of (ξ, λ, xᵢₙᵢ). The profile likelihood in λ is flat down to λ = 0, and the full fit improvement over (Δχ²ₘᵢₙ = -5.18, mock-calibrated $p = 0.013$ / 2.2σ, Bayes factor ln B = +0.12 ± 0.22) is already accessible at ξ = 0. Local-Gravity Consistency: Tracks the light-scalar Brans–Dicke Cavendish coupling, PPN γ, and Ġ/G per posterior sample. Only 1.9% of the cosmology-only posterior satisfies the Cassini bound (γ - 1 < 2.3 × 10⁻⁵); when Cassini is enforced as a prior, the posterior collapses to minimally coupled exponential quintessence (ξ = 0.000 ± 0.002). Included Materials Full MCMC chains (unflattened emcee ensembles and dynesty nested-sampling runs) including derived quantities (Γ₀, PPN γ, Ġ/G, G(zᵢ)/G₀). Complete reproduction scripts, likelihood wrappers, and test suites for DESI DR2 BAO and Pantheon+/Dovekie. Pipeline manifests, run logs, and figure/table generation code.