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Abstract Radio free–free emission is considered to be one of the most reliable tracers of star formation in galaxies. However, as it constitutes the faintest part of the radio spectrum—being roughly an order of magnitude less luminous than radio synchrotron emission at the GHz frequencies typically targeted in radio surveys—the usage of free–free emission as a star formation rate tracer has mostly remained limited to the local universe. Here, we perform a multifrequency radio stacking analysis using deep Karl G. Jansky Very Large Array observations at 1.4, 3, 5, 10, and 34 GHz in the COSMOS and GOODS-North fields to probe free–free emission in typical galaxies at the peak of cosmic star formation. We find that z ∼ 0.5–3 star-forming galaxies exhibit radio emission at rest-frame frequencies of ∼65–90 GHz that is ∼1.5–2 times fainter than would be expected from a simple combination of free–free and synchrotron emission, as in the prototypical starburst galaxy M82. We interpret this as a deficit in high-frequency synchrotron emission, while the level of free–free emission is as expected from M82. We additionally provide the first constraints on the cosmic star formation history using free–free emission at 0.5 ≲ z ≲ 3, which are in good agreement with more established tracers at high redshift. In the future, deep multifrequency radio surveys will be crucial in order to accurately determine the shape of the radio spectrum of faint star-forming galaxies, and to further establish radio free–free emission as a tracer of high-redshift star formation. 

We report the serendipitous discovery of a dusty, starbursting galaxy at z=5.667 (called CRLE hereafter), in close physical association to the "normal" Main Sequence galaxy HZ10 at z=5.654. CRLE was identified by detection of [CII], [NII] and CO(2-1) line emission, making it the highest redshift, most luminous starburst in the COSMOS field. This massive, dusty galaxy appears to be forming stars at a rate of at least 1500$$\,M_\odot$$ yr$$^{-1}$$ in a compact region only ~3 kpc in diameter. The dynamical and dust emission properties of CRLE suggest an ongoing merger driving the starburst, in a potentially intermediate stage relative to other known dusty galaxies at the same epoch. The ratio of [CII] to [NII] may suggest that an important contribution to the [CII] emission comes from a diffuse ionized gas component, which could be more extended than the dense, starbursting gas. CRLE appears to be located in a significant galaxy overdensity at the same redshift, potentially associated with a large scale cosmic structure recently identified in a Lyman Alpha Emitter survey. This overdensity suggests that CRLE and HZ10 reside in a protocluster environment, offering the tantalizing opportunity to study the effect of a massive starburst on protocluster star formation. Our findings support the interpretation that a significant fraction of the earliest galaxy formation may occur from the inside-out, within the central regions of the most massive halos, while rapidly evolving into the massive galaxy clusters observed in the local Universe.