SCRIPT in the Cosmic Dawn: Distinguishing Redshift-Evolving Galaxy Populations with 21-cm Fluctuations

Recent James Webb Space Telescope (JWST) observations suggest an unexpectedly high abundance of luminous galaxies at $z \gtrsim 10$, challenging traditional models of star formation. The 21-cm signal of neutral hydrogen offers a complementary, volume-averaged probe of these early epochs. In this work, we present a major extension to the explicitly photon-conserving semi-numerical framework SCRIPT, enabling the self-consistent calculation of spin temperature fluctuations driven by inhomogeneous Lyman-$\alpha$ coupling and X-ray heating during the Cosmic Dawn. Using this framework, we compare a JWST-informed fiducial galaxy model, featuring a redshift-evolving star-formation efficiency, against a static baseline model. We demonstrate that the global 21-cm signal is highly degenerate: a static galaxy population can replicate the absorption trough of an evolving population if a steep, mass-dependent X-ray efficiency is invoked to shift intergalactic medium heating toward highly abundant, low-mass halos. However, this degeneracy is definitively broken by the 21-cm power spectrum. Because spatial fluctuations retain a structural memory of the clustering bias of the source halos, the tuned static model predicts a substantially lower power spectrum amplitude across all characteristic peaks. We conclude that combining global and fluctuation measurements is essential to robustly constrain the redshift evolution of high-redshift galaxies.