  We present a quantitative model of Lyman-alpha (Ly-alpha) emission throughout
cosmic history and determine the prospects for intensity mapping of spatial
fluctuations in the Ly-alpha signal. Since i) our model assumes at z>6 the
minimum star formation required to sustain reionization and ii) is based at z<6
on a luminosity function extrapolated from the few observed bright Ly-alpha
emitters, this should be considered a lower limit. Mapping the line emission
allows probes of reionization, star formation, and large-scale structure (LSS)
as a function of redshift. While Ly-alpha emission during reionization has been
studied, we also predict the post-reionization signal to test predictions of
the intensity and motivate future intensity mapping probes of reionization. We
include emission from massive dark matter halos and the intergalactic medium
(IGM) in our model. We find agreement with current, measured luminosity
functions of Ly-alpha emitters at z<8. However, diffuse IGM emission, not
associated with Ly-alpha emitters, dominates the intensity up to z~10. While
our model is applicable for deep-optical or near-infrared observers like the
SuMIre survey or the James Webb Space Telescope, only intensity mapping will
detect the diffuse IGM emission. We also construct a 3D power spectrum model of
the Ly\alpha emission, and characterize possible foreground contamination.
Finally, we study the prospects of an intensity mapper for measuring Ly-alpha
fluctuations while identifying interloper contamination for removal. Our
results suggest that while the reionization signal is challenging, Ly-alpha
fluctuations can be an interesting new probe of LSS at late times when used in
conjunction with other lines like, e.g., H-alpha, to monitor low-redshift
foreground confusion.
