Probing initial isocurvature perturbation with 21cm one-point statistics

Isocurvature perturbation--expected from multi-field inflation models--can leave unique signatures in the early Universe, but remain weakly constrained, especially on small scales. In this work, we investigate the constraining power of one-point statistics (variance and skewness) of the 21cm brightness temperature during Cosmic Dawn and the Epoch of Reionization, using semi-numerical simulations from 21cmFAST. We model both adiabatic and cold dark matter isocurvature modes, exploring their impact on the matter power spectrum, the timing of structure formation, and the evolution of neutral hydrogen. By varying astrophysical parameters as well as the isocurvature fraction and spectral index, we quantify their respective effects on the 21cm power spectrum and on one-point statistics, using the former as a physical diagnostic and the latter as the basis of our final forecast. Our results show that while variance is highly sensitive to the timing of cosmic events and provides tight constraints on isocurvature parameters, skewness is more strongly affected by astrophysical uncertainties and observational noise. Incorporating realistic instrumental noise based on SKA configurations, we perform a Fisher analysis using only the redshift evolution of the one-point statistics, and demonstrate that the isocurvature fraction can be constrained down to the percent level, though a strong degeneracy with the spectral index remains. We discuss the importance of complementary probes, such as the 21cm forest and galaxy surveys, to break these parameter degeneracies. Our findings highlight the power of 21cm one-point statistics as robust and independent tools for probing early-Universe physics beyond what is accessible with traditional power spectrum analyses.