Stellar populations dominated by massive stars in dusty starburst galaxies across cosmic time.

All measurements of cosmic star formation must assume an initial distribution of stellar masses-the stellar initial mass function-in order to extrapolate from the star-formation rate measured for typically rare, massive stars (of more than eight solar masses) to the total star-formation rate across the full stellar mass spectrum . The shape of the stellar initial mass function in various galaxy populations underpins our understanding of the formation and evolution of galaxies across cosmic time . Classical determinations of the stellar initial mass function in local galaxies are traditionally made at ultraviolet, optical and near-infrared wavelengths, which cannot be probed in dust-obscured galaxies, especially distant starbursts, whose apparent star-formation rates are hundreds to thousands of times higher than in the Milky Way, selected at submillimetre (rest-frame far-infrared) wavelengths. The C/O isotope abundance ratio in the cold molecular gas-which can be probed via the rotational transitions of the CO and CO isotopologues-is a very sensitive index of the stellar initial mass function, with its determination immune to the pernicious effects of dust. Here we report observations of CO and CO emission for a sample of four dust-enshrouded starbursts at redshifts of approximately two to three, and find unambiguous evidence for a top-heavy stellar initial mass function in all of them. A low CO/CO ratio for all our targets-alongside a well tested, detailed chemical evolution model benchmarked on the Milky Way -implies that there are considerably more massive stars in starburst events than in ordinary star-forming spiral galaxies. This can bring these extraordinary starbursts closer to the 'main sequence' of star-forming galaxies , although such main-sequence galaxies may not be immune to changes in initial stellar mass function, depending on their star-formation densities.