  The intensity of the Cosmic UV background (UVB), coming from all sources of
ionising photons such as star-forming galaxies and quasars, determines the
thermal evolution and ionization state of the intergalactic medium (IGM) and
is, therefore, a critical ingredient for models of cosmic structure formation.
Most of the previous estimates are based on the comparison between observed and
simulated Lyman-$\alpha$ forest. We present the results of an independent
method to constrain the product of the UVB photoionisation rate and the
covering fraction of Lyman limit systems (LLSs) by searching for the
fluorescent Lyman-$\alpha$ emission produced by self-shielded clouds. Because
the expected surface brightness is well below current sensitivity limits for
direct imaging, we developed a new method based on three-dimensional stacking
of the IGM around Lyman-$\alpha$ emitting galaxies (LAEs) between 2.9<z<6.6
using deep MUSE observations. Combining our results with covering fractions of
LLSs obtained from mock cubes extracted from the EAGLE simulation, we obtain
new and independent constraints on the UVB at z>3 that are consistent with
previous measurements, with a preference for relatively low UVB intensities at
z=3, and which suggest a non-monotonic decrease of $\Gamma$HI with increasing
redshift between 3<z<5. This could suggest a possible tension between some UVB
models and current observations which however require deeper and wider
observations in Lyman-$\alpha$ emission and absorption to be confirmed.
Assuming instead a value of UVB from current models, our results constrain the
covering fraction of LLSs at 3<z<4.5 to be less than 25% within 150kpc from
LAEs.
