After inflation, the Universe presumably undergoes a phase of reheating which in effect starts the thermal big bang cosmology. 

However, so far we have very little direct experimental or observational evidence of this important phase of the Universe.

I would like to argue that measuring the spectrum of freely propagating relativistic particles produced during reheating may provide us with powerful information on the reheating phase. To demonstrate this possibility, we first discuss which kind of (SM,BSM) particle can play the role of the messenger of reheating. Then we show that the spectrum crucially depends on whether the mother non-relativistic particle once dominated the Universe or not. Characteristic features caused by the dependence on the number of the relativistic degrees of freedom may even allow to infer the temperature when the decay of the heavy particle occurred. This talk is based on arXiv:2007.15006 and 2102.00006.