A Phenomenological Interacting Dark Energy Model: Stage I Constraints from Low-Redshift Data

Stage I preprint (bilingual EN/RU), version 1.0.2. We study a minimal interacting dark energy (IDE) model with a scalar field φ in a quadratic potential and a conformal coupling to dark matter. The Stage I goal is to derive the background and linear perturbation equations, obtain preliminary constraints from low-z data, and test for periodic modulations in H(z) as a separate phenomenological probe (independent of any freeze-in assumption). Data: MCMC on the baseline catalogue of 24 H(z) + 10 fσ8 points (N=34); extended robustness check on 38 H(z) (32 Cosmic Chronometers + 6 DESI DR2 BAO) + 23 fσ8. DESI DR2 BAO is included with diagonal covariance only. Main results (baseline MCMC): β = 0.015 with 68% CI [0.002, 0.103]; log10(mφ/eV) = −32.00 with 68% CI [−33.35, −30.64]; H0 = 67.7 km s−1 Mpc−1 with 68% CI [65.7, 69.9]. The model is essentially degenerate with ΛCDM at the best-fit point (Δχ2 ≈ 0). No significant periodic signal in H(z): effective amplitude C ≃ 5.5 km s−1 Mpc−1 (68% CI [3.0, 8.4]); 84% upper edge C < 8.4; information criteria prefer ΛCDM. Files: IDE_StageI_EN.pdf (primary), IDE_StageI_RU.pdf, IDE_StageI_code_data.zip (reproducibility archive). Full CMB / Boltzmann analysis is deferred to Stage II.