RMB Cosmology: Official Euclid Predictions (2026–2027)

This compact prediction sheet provides the official Euclid falsification reference for RMB cosmology (Space–Matter–Motion Theory). RMB predicts regime-dependent, percent-level deviations from the best-fit ΛCDM baseline, activated in the intermediate-redshift late universe with minimal effective backreaction (Omega_RMB,eff ≈ 1.8% today) and suppressed at early times through dynamical screening. The decisive Euclid test lies in quasi-linear large-scale structure clustering near k ≈ 0.1 h Mpc^-1 and in the joint growth–lensing window 0.3 ≲ z ≲ 2, where RMB predicts correlated signatures: Growth enhancement in the growth rate fσ8(z) at the +1% to +3% level Weak-lensing suppression in S8 at the -1% to -2% level Strict consistency with the bound |ΔP/P| ≤ 10% at quasi-linear scales Primary falsification criterion: If Euclid measures |ΔP/P| > 10% at k ≈ 0.1 h Mpc^{-1}, or if no percent-level growth/lensing deviation is detected in the predicted intermediate-redshift window (0.3 < z < 2), the RMB framework is ruled out. This note is derived from the RMB core formulation and the conservative weak-screening cosmological baseline established in RMB Cosmology III–IV (Dellomonaco, Zenodo 2025–2026). It is intended as a direct, mission-facing prediction reference for Euclid data releases in 2026–2027.