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Using analytical models and cosmological  N ‐body simulations, we study the free–free radio emission from ionized gas in clusters and groups of galaxies. The results obtained with the simulations are compared with analytical predictions based on the mass function and scaling relations. Earlier works based on analytical models have shown that the average free–free signal from small haloes (galaxies) during and after the reionization time could be detected with future experiments as a distortion of the cosmic microwave background (CMB) spectrum at low frequencies ( ν &lt; 5  GHz). We focus on the period after the reionization time (from redshift   z = 0 to 7 ) and on haloes that are more massive than in previous works (groups and clusters). We show how the average signal from haloes with   M  &gt; 10 13   h  −1   M ⊙   is less than 10 per cent the signal from the more abundant and colder smaller mass haloes. However, the individual signal from the massive haloes could be detected with future experiments opening the door for a new window to study the intracluster medium.

The cosmological free–free signal from galaxy groups and clusters