Modeling Post-Reionization HI Distributions in Fuzzy Dark Matter Cosmologies Using Conditional Normalizing Flows

Upcoming 21 cm intensity mapping experiments like the Square Kilometer Array (SKA) hold significant potential to constrain the properties of dark matter. In this work, we model neutral hydrogen (HI) distributions using high-resolution hydrodynamical $N$-body simulations of both cold dark matter (CDM) and fuzzy dark matter (FDM) cosmologies in the post-reionization redshift range of $z=3.42-4.94$. We show that the HI abundance decreases in FDM-like cosmologies. Extreme FDM models with $m\sim 10^{-22}$ eV are at odds with a range of measurements. Due to the increased halo bias, the HI bias increases, paralleled by the damped Lyman-$\alpha$ (DLA) bias which we infer from the cross-section of DLAs. The distribution of the latter in extreme FDM models has a high median at the low-mass end, which can be traced to the high column density of cosmic filaments. FDM models exhibit a very similar abundance of DLAs compared to CDM while sub-DLAs are already less abundant. We study the prospects of detecting the brightest HI peaks with SKA1-Low at $z=4.94$, indicating moderate signal-to-noise ratios (SNR) at angular resolution $\theta_A = 2^{\prime}$ with a rapidly declining SNR for lower values of $\theta_{A}$. After training the conditional normalizing flow network HIGlow on 2D HI maps, we interpolate its latent space of axion masses to predict the peak flux for a new, synthetic FDM cosmology, finding good agreement with expectations. This work thus underscores the potential of normalizing flows in capturing complex, non-linear structures within HI maps, offering a versatile tool for conditional sample generation and prediction tasks.