Universal Hyperuniformity in Active Field Theories

We show that dry scalar-order active field theories (AFTs) are universally hyperuniform, i.e., density fluctuations are anomalously suppressed in the long-time limit regardless of the integrability or functional form of the active contributions up to third order in gradient terms. These AFTs include Active model B, Active model B+, and effective Cahn-Hilliard models. Moreover, density variances and spectral densities are virtually indistinguishable from that of passive phase-separated hyperuniform fields. Higher moments of the density fluctuations, however, reveal activity-dependent higher-order correlations that are not captured by conventional two-point measures that characterize hyperuniformity.