Scale-Dependent Clustering Suppression from Late-Time Dark Matter Pressure: CLASS Implementation, Validation Protocol, and First Results

This technical report presents a CLASS Boltzmann code implementation of a pressure-bearing dark matter model derived from the BigSnap scalar field framework, together with a pre-committed validation protocol and first numerical results. The model is characterized by a time-dependent dark matter equation of state w_dm(a) = −r·a³/(4Ω_R0) and an effective perturbation sound speed c_s²(a) = |w_dm(a)|^γ. The a³γ scaling produces a late-time, scale-dependent Jeans suppression of structure growth while leaving CMB scales unaffected. All runs use identical initial conditions and cosmological parameters to the ΛCDM reference (Planck 2018 best-fit values). The only non-standard inputs are bigsnap_r and bigsnap_gamma. No parameters were retuned to fit any observable. First numerical results: For r = 4×10⁻⁴ and γ = 1.5, the implementation yields σ₈ = 0.780 compared to the ΛCDM reference σ₈ = 0.822 (5.1% suppression). A full (r, γ) parameter scan over 30 combinations identifies a continuous viable region near γ ≈ 1.5, r ≈ 3–5×10⁻⁴. γ = 1.0 produces massive oversuppression at all r values. γ = 2.0 produces negligible suppression. Only γ ≈ 1.5 naturally populates the observed S₈ range, indicating a localized preferred region in parameter space rather than a broad degeneracy. Eight validation checks passed: ΛCDM recovery: σ₈ = 0.8224 at r = 0 Resolution: stable at Nloga = 3000, 6000, 12000 CMB TT: 0.007% max deviation (threshold 1%) CMB lensing: 0.075% max deviation (threshold 0.1%) Redshift evolution: 0.0% suppression at z=2, 5.1% at z=0 fσ₈: 0.9% deviation at z=0.5, within current ~2–4% measurement precision BAO peak: 0.009% shift, an order of magnitude below survey sensitivity Sub-horizon gauge: corrections < 0.0002% at the σ₈-dominant scale KiDS-1000 S₈ comparison: ΛCDM predicts S₈ = 0.843, which is 3.85σ from the KiDS-1000 measurement (S₈ = 0.766 ± 0.020). The best-fit BigSnap point gives S₈ = 0.785 (0.94σ from KiDS), improving the fit by Δχ² ≈ 13.8 — roughly a ~3σ-level preference after accounting for two additional parameters. The improvement is not diffuse: only γ ≈ 1.5 lands in the KiDS-preferred range. Hubble tension: The a³ scaling ensures w_dm(a_rec) ~ 10⁻¹⁵ at recombination. The sound horizon shifts by −0.015% and H₀ shifts by 0.0000 km/s/Mpc. The Hubble tension is not addressed by this mechanism. This is a structural limitation, not a parameter choice: the same scaling that makes the CMB safe prevents any lever arm on the sound horizon. Scope: The model passes all implemented validation checks and is consistent with current observational precision for key summary observables. This does not constitute a claimed resolution of the S₈ tension, nor does it replace a full likelihood analysis against combined datasets. The correct interpretation is that the mechanism produces suppression consistent with the observed S₈ discrepancy for r ≈ 3–5×10⁻⁴ at γ ≈ 1.5, with no detected conflicts at current precision. This deposit records the pre-committed predictions, validation protocol, and first results prior to any likelihood analysis. Companion framework paper: Snider, D., "The Big Snap," Zenodo (2026).