Topological Signatures of Heating and Dark Matter in the 21 cm Forest

Abstract: We show that the topology of the 21 cm forest carries cosmological information that is inaccessible to traditional amplitude- or correlation-based statistics. Applying topological data analysis to simulated spectra spanning a range of X-ray heating efficiencies and dark-matter free-streaming scales, we compute persistence diagrams and Betti-0 curves that describe the formation and merger hierarchy of absorption troughs. A small set of interpretable descriptors (trough-line density, lifetime variance, and lifetime skewness) respond in nearly orthogonal directions across the (f_X, m_WDM) parameter space, enabling a substantial reduction of the degeneracy between heating and dark-matter suppression. These topological signatures remain detectable under SKA1-Low-like thermal noise, demonstrating that topology provides a stable and non-Gaussian probe of small-scale physics during Cosmic Dawn.