A large fraction of the baryonic matter in the Universe is located in filaments in the intergalactic medium (IGM). 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. Here we simulate the intensity and spatial fluctuations in Lyman alpha (Lyα) emission from filaments in the IGM and discuss the prospects for the next generation of space-based instruments to detect the low-surface brightness Universe at ultraviolet (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 Lyα emissivity is then estimated, taking into account recombination and collisional excitation processes. We find that the detection of these filaments through their Lyα 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 Lyα 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 Lyα emission line and discuss how this continuum can affect observations.