Isotonic-Thawing Quintessence with Canonical Perturbations: Transient Acceleration, Native CAMB Spectra, Growth, and a DESI DR2–Pantheon+–CMBComp Posterior

Abstract

We study a canonical, non-phantom thawing quintessence model defined by the coefficient-locked isotonic potential V(Φ) = Λ₀(Φ/2 − 2/Φ)², where Φ = φ/M_Pl. The locking completes an exact square, so V ≥ 0 with a unique regular zero-energy minimum at Φ = 2 and no residual vacuum-energy floor; in the positive weight variable Q = Φ²/4 = e^ψ the same shape reads V/Λ₀ = 2(cosh ψ − 1). A branch-specific two-measure construction can generate this completed form algebraically, but the inference presented here uses only ordinary canonical quintessence and claims no UV completion. The model adds one parameter to flat ΛCDM: the bounded displacement coordinate η = 2/Φᵢ, with ΛCDM nested at η = 0 and the potential amplitude fixed by spatial flatness at every sampled point. A deterministic quadrature posterior combining DESI DR2 BAO, an 11-knot Pantheon+ distance compression, and the CMBComp CMB-3w compression gives a best fit at η = 0.403405 (Φᵢ = 4.95779), with (w₀, wₐ) = (−0.948924, −0.078448) and Δχ² = −1.9433 for one additional parameter. The corresponding ΔAIC = +0.0567 and ΔBIC = +1.3525: the model remains observationally viable and close to ΛCDM, but model selection is neutral and the ΛCDM boundary stays inside the posterior support. Exact phase-plane evaluation places both calibrated histories inside the Caldwell–Linder thawing band at the present epoch, (1+w, w′) = (0.0511, 0.0784) at the best fit, confirming bona fide thawing behaviour while showing that the one-parameter locus is a curve rather than a free CPL plane. Because V_min = 0, the finite-displacement branch cannot settle into eternal de Sitter acceleration. Direct integration of the same field equations into the future, with no CPL extrapolation, ends acceleration at a = 13.88, about 60.3 Gyr from the present, and at a = 2.86 (21.1 Gyr) for the original Φᵢ = 4 benchmark. Both exits precede the first crossing of the minimum, after which the field enters damped quadratic oscillations with ⟨w⟩ → 0 and ρ ∝ a⁻³, leaving a decelerating expansion with no de Sitter event horizon. A censored push-forward of the posterior yields an exit-time survival function assigning 37.8% probability to an exit within 100 Gyr and 78.7% within 1 Tyr. The exact histories are executed natively in CAMB 1.6.6 with tabulated non-phantom w(a), c_s² = 1, and zero anisotropic stress, with no constant-w, CPL, or PPF fallback. For 30 ≤ ℓ ≤ 2500 the best fit differs from matched ΛCDM by at most 0.217% in TT,

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