  A large fraction of the baryonic matter in the Universe is located in
filaments in the intergalactic medium. However, the low surface brightness of
these filaments has not yet allowed their direct detection except in very
special regions in the circum-galactic medium (CGM). Here we simulate the
intensity and spatial fluctuations in Lyman Alpha ${\rm (Ly\alpha)}$ emission
from filaments in the intergalactic medium (IGM) and discuss the prospects for
the next generation of space based instruments to detect the low surface
brightness universe at UV wavelengths. Starting with a high resolution N-body
simulation we obtain the dark matter density fluctuations and associate baryons
with the dark matter particles assuming that they follow the same spatial
distribution. The IGM thermal and ionization state is set by a model of the UV
background and by the relevant cooling processes for a hydrogen and helium gas.
The ${\rm Ly\alpha}$ emissivity is then estimated, taking into account
recombination and collisional excitation processes. We find that the detection
of these filaments through their ${\rm Ly\alpha}$ emission is well in the reach
of the next generation of UV space based instruments and so it should be
achieved in the next decade. The density field is populated with halos and
galaxies and their ${\rm Ly\alpha}$ emission is estimated. Galaxies are treated
as foregrounds and so we discuss methods to reduce their contamination from
observational maps. Finally, we estimate the UV continuum background as a
function of the redshift of the ${\rm Ly\alpha}$ emission line and discuss how
this continuum can affect observations.
