The MUSE view of the Frontier Field clusters

Strong gravitational magnification in the core of lensing clusters allows to probe the faint-end of the galaxy luminosity function up to very high redshift. In particular, the Frontier Fields have allowed us to identify a large number of faint dropouts and constrain the Lyman-break luminosity function at z~5-7. I present here the results of an ongoing program with MUSE, a new integral field spectrograph on the Very Large Telescope having a large field of view (1 arcmin2), to confirm these candidate high redshift dropouts through Lyman-α emission and identify additional emitters with high equivalent width, fainter than the depth of the Frontier Fields Hubble images. Combined with similar deep exposures taken with MUSE in blank fields, this gives us the best opportunity to probe the Lyman-α luminosity function over a wide range in luminosity.