Cosmological simulations suggest that most of the matter in the Universe is distributed along filaments connecting galaxies .
Illuminated by the cosmic UV background ( UVB ) , these structures are expected to glow in fluorescent Ly \alpha emission with a Surface Brightness ( SB ) that is well below current observational limits for individual detections .
Here , we perform a stacking analysis of the deepest MUSE/VLT data using three-dimensional regions ( subcubes ) with orientations determined by the position of neighbouring Ly \alpha galaxies ( LAEs ) at 3 < z < 4 .
Our method should increase the probability of detecting filamentary Ly \alpha emission , provided that these structures are Lyman Limit Systems ( LLSs ) .
By stacking 390 oriented subcubes we reach a 2 \sigma sensitivity level of \mathrm { SB } \approx 0.44 \times 10 ^ { -20 } erg s ^ { -1 } cm ^ { -2 } arcsec ^ { -2 } in an aperture of 1 \mathrm { arcsec ^ { 2 } } \times 6.25 \mathrm { \AA } , which is three times below the expected fluorescent Ly \alpha signal from the Haardt-Madau 2012 ( HM12 ) UVB at z \sim 3.5 .
No detectable emission is found on intergalactic scales , implying that at least two thirds of our subcubes do not contain oriented LLSs for a HM12 UVB .
On the other hand , significant emission is detected in the circum-galactic medium ( CGM ) of galaxies in the direction of the neighbours .
The signal is stronger for galaxies with a larger number of neighbours and appears to be independent of any other galaxy properties such as luminosity , redshift and neighbour distance .
We estimate that preferentially oriented satellite galaxies can not contribute significantly to this signal , suggesting instead that gas densities in the CGM are typically larger in the direction of neighbouring galaxies on cosmological scales .