CoreLumen Observational Series V : Forecast Constraints on Late-Time Growth Deformation

This record presents a forecast analysis for the late-time growthdeformation parameter p1 within the CoreLumen observational pipeline. COS V extends the likelihood framework developed in COS IV-B2,which combined BAO, RSD, Planck priors, CMB lensing, and weak lensingconstraints. The present stage evaluates the expected improvementin parameter constraints under future survey precision. The forecast likelihood replaces the current weak-lensing uncertaintywith an anticipated precision level for the S8 parameter S8 = σ8 √(Ωm / 0.3). The likelihood used in the forecast analysis is χ² = χ²_BAO + χ²_RSD + χ²_Planck + χ²_CMB lensing + χ²_WL,forecast. The parameter space explored is (p1, σ8, Ωm). The resulting best-fit parameters remain consistent with those obtainedin COS IV-B2 p1 ≈ −0.25σ8 ≈ 0.80Ωm ≈ 0.30 while the allowed parameter region becomes significantly smaller due tothe improved observational precision. The forecast demonstrates that future large-scale structure surveyscould substantially tighten constraints on the late-time growthdeformation parameter. This document serves as an archival record of the COS V forecastanalysis within the CoreLumen observational program and is notintended as a journal submission.