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Planet formation theories predict a large but still undetected population ofshort-period terrestrial planets orbiting brown dwarfs. Should specimens ofthis population be discovered transiting relatively bright and nearby browndwarfs, the Jupiter-size and the low luminosity of their hosts would make themexquisite targets for detailed atmospheric characterisation with JWST andfuture ground-based facilities. The eventual discovery and detailed study of asignificant sample of transiting terrestrial planets orbiting nearby browndwarfs could prove to be useful not only for comparative exoplanetology butalso for astrobiology, by bringing us key information on the physicalrequirements and timescale for the emergence of life.  In this context, we present a search for transit-signals in archivaltime-series photometry acquired by the Spitzer Space Telescope for a sample of44 nearby brown dwarfs. While these 44 targets were not particularly selectedfor their brightness, the high precision of their Spitzer light curves allowsus to reach sensitivities below Earth-sized planets for 75% of the sample anddown to Europa-sized planets on the brighter targets. We could not identify anyunambiguous planetary signal. Instead, we could compute the first limits on thepresence of planets on close-in orbits. We find that within a 1.28 day orbit,the occurrence rate of planets with a radius between 0.75 and 3.25 R$_\oplus$is {\eta} < 67 $\pm$ 1%. For planets with radii between 0.75 and 1.25R$_\oplus$, we place a 95% confident upper limit of {\eta} < 87 $\pm$ 3%. If weassume an occurrence rate of {\eta} = 27% for these planets with radii between0.75 and 1.25 R$_\oplus$, as the discoveries of the Kepler-42b and TRAPPIST-1bsystems would suggest, we estimate that 175 brown dwarfs need to be monitoredin order to guarantee (95%) at least one detection.

First limits on the occurrence rate of short-period planets orbiting brown dwarfs