  We use a new method to model fluctuations of the Lyman-Werner (LW) and
Lyman-alpha radiation backgrounds at high redshift. At these early epochs the
backgrounds are symptoms of a universe newly lit with its first stars. LW
photons (11.5-13.6 eV) are of particular interest because they dissociate
molecular hydrogen, the primary coolant in the first minihalos. By using a
variation of the halo model, we efficiently generate power spectra for any
choice of radiation background. We find that the LW power spectrum typically
traces the matter power spectrum at large scales but turns over at the scale
corresponding to the effective `horizon' of LW photons (~100 comoving Mpc),
unless the sources are extremely rare. The series of horizons that characterize
the Lyman-alpha flux profile shape the fluctuations of that background in a
similar fashion, though those imprints are washed out once one considers
fluctuations in the brightness temperature of the 21-cm signal. The Lyman-alpha
background strongly affects the redshifted 21-cm signal at just about the time
the LW background begins to dissociate molecular hydrogen, so measuring that
background's properties will reveal important information about the transition
from early Population III stars to more normal stars. Around this time we find
that fluctuations in the LW background are weak; the fractional standard
deviation is less than ~0.5 on scales > 10 cMpc, only rising to be of order
unity on scales < 1 cMpc. This should not lead to substantial spatial
fluctuations in molecular hydrogen content, except at the earliest times. Even
then, most halos form far from other sources, so the transition from star
formation in low-mass to high-mass halos is rather homogeneous across the
universe.
