J. Willingham, A. Hopkins, T. Zafar, J. Afonso, U. T. Ahmed, A. Ahmad, A. Battisti, D. Bomans, M. J. I. Brown, M. Cowley, D. Farrah, T. J. Galvin, B. Holwerda, D. Leahy, U. Maio, T. Mukherjee, J. Prathap, N. Seymour, J. Th. van Loon, E. Ward

We present a novel approach to correcting H$α$ luminosity functions for dust extinction by calibrating against radio-based star formation rates (SFRs), using data from the Evolutionary Map of the Universe (EMU) and Galaxy and Mass Assembly (GAMA) surveys. Accurate dust correction is essential for deriving SFRs from rest-frame UV-optical emission lines, particularly as the \textit{James Webb Space Telescope} extends such measurements to galaxies at $z>5$. While a luminosity dependence of dust obscuration has long been recognised, our method exploits the empirical relationship between obscured (H$α$) and unobscured (radio) SFRs to provide a dust correction that can be applied where traditional spectroscopic techniques, e.g. Balmer line based approaches, are unavailable. We apply the SFR based dust correction to 25 published H$α$ luminosity functions spanning $0<z<8$, and derive corresponding star formation rate densities (SFRDs). Adopting the locally calibrated H$α$--radio relation ends up with an overestimate of the cosmic SFRD by more than two orders of magnitude at $z\gtrsim1$. Motivated by the luminosity dependent relation in the local Universe, we introduce a new model where the luminosity dependence of the dust obscuration decreases with increasing redshift. This approach can reproduce observed SFRDs across cosmic time. These results highlight the potential of a radio-based calibration for dust correction, where a luminosity dependent correction would need to decline in strength with increasing redshift. This implies that the dust content or distribution in galaxies at early epochs differs substantially from that in the local Universe.