From RSD to Clusters: A Parameter-Locked Test of Late-Time Structure Growth

We present a cross-probe test of late-time cosmic structure growth by propagating redshift-space distortion (RSD) constraints on the effective gravitational coupling μ(z) into galaxy cluster abundance predictions. Using the growth modification amplitude αₗ₂ = 0.34 ± 0.16 derived from BOSS DR12 BAO+RSD measurements, we compute the expected cluster mass function under a late-time enhanced growth scenario with no parameters fit to cluster data. Under CMB-consistent primordial normalization, the model predicts a +6% excess in total cluster counts relative to ΛCDM in the eRASS1 mass and redshift range (M > 10¹⁴ M☉, 0.1 < z < 0.8). More importantly, it produces a distinctive redshift-dependent tilt in the cluster redshift distribution. The normalized shape ratio 𝓡(z) = R_model(z) / R_ΛCDM(z) transitions from >1 at low redshift to