Structural Differentiation Cosmology v2.0: Observable Signatures and the Geometry–Growth Projection Test (GGPT)

This work presents the predicted observable signatures of Structural Differentiation Cosmology / Structural Differentiation Gravity (SDC/SDG v2.0).

The central prediction is a decoupling between background expansion geometry and structure growth. While the Hubble expansion H(z) remains nearly degenerate with a ΛCDM-like reference model, the growth observable fσ8(z) exhibits a systematic suppression at intermediate redshift.

This behavior is summarized through the Geometry–Growth Projection Test (GGPT), defined as a joint diagnostic in the (ΔH/H, Δ(fσ8)/fσ8) plane. The GGPT provides a compact and directly falsifiable representation of the model’s predictions.

Key predicted features include:
- Near-degeneracy of H(z) with ΛCDM
- Redshift-dependent suppression of structure growth
- Peak deviation at intermediate redshift (z ≈ 1–1.5)
- A characteristic trajectory in the GGPT plane separating geometry and growth

The included figure provides a unified visualization of these signatures. Mock data shown are generated from theoretical expectations with assumed observational uncertainties and are intended for illustration only.

This work serves as a timestamped prediction prior to comparison with future observational surveys such as Euclid, DESI, and Rubin/LSST.

If future observations reproduce the predicted GGPT structure, the model is supported; otherwise, it is falsified.