  We discuss how one can reconstruct the thermal history of the Universe by
combining cosmic microwave background (CMB) measurements and gravitational wave
(GW) direct detection experiments. Assuming various expansion eras to take
place after the inflationary reheating and before Big-Bang Nucleosynthesis
(BBN), we show how measurements of the GW spectrum can be used to break the
degeneracies associated with CMB data, the latter being sensitive to the total
amount of cosmic expansion only. In this context, we argue that the expected
constraints from future CMB and GW experiments can probe a scenario in which
there exists late-time entropy production in addition to the standard
reheating. We show that, for some cases, combining data from future CMB and GW
direct detection experiments allows the determination of the reheating
temperature, the amount of entropy produced and the temperature at which the
standard radiation era started.
