  We demonstrate a new approach for the metrology of microwave fields based on
the trap-loss-spectroscopy of cold Rydberg atoms in a magneto-optical trap.
Compared to state-of-the-art sensors using room-temperature vapors, cold atoms
allow longer interaction times, better isolation from the environment and a
reduced Doppler effect. Our approach is particularly simple as the detection
relies on fluorescence measurements only. Moreover, our signal is well
described by a two-level model across a broad measurement range, allowing in
principle to reconstruct the amplitude and the frequency of the microwave field
simultaneously without the need for an external reference field. We report on a
scale factor linearity at the percent level and no noticeable drifts over two
hours, paving the way for new applications of cold Rydberg atoms in metrology
such as calibrating blackbody shifts in state-of-the-art optical clocks,
monitoring the Earth cryosphere from space, measuring the cosmic microwave
background or searching for dark matter.
