The high-redshift 21-cm signal of neutral hydrogen is expected to be observed
within the next decade and will reveal epochs of cosmic evolution that have
been previously inaccessible. Due to the lack of observations, many of the
astrophysical processes that took place at early times are poorly constrained.
In recent work we explored the astrophysical parameter space and the resulting
large variety of possible global (sky-averaged) 21-cm signals. Here we extend
our analysis to the fluctuations in the 21-cm signal, accounting for those
introduced by density and velocity, LyΞ± radiation, X-ray heating, and
ionization. While the radiation sources are usually highlighted, we find that
in many cases the density fluctuations play a significant role at intermediate
redshifts. Using both the power spectrum and its slope, we show that properties
of high-redshift sources can be extracted from the observable features of the
fluctuation pattern. For instance, the peak amplitude of ionization
fluctuations can be used to estimate whether heating occurred early or late
and, in the early case, to also deduce the cosmic mean ionized fraction at that
time. The slope of the power spectrum has a more universal redshift evolution
than the power spectrum itself and can thus be used more easily as a tracer of
high-redshift astrophysics. Its peaks can be used, for example, to estimate the
redshift of the LyΞ± coupling transition and the redshift of the heating
transition (and the mean gas temperature at that time). We also show that a
tight correlation is predicted between features of the power spectrum and of
the global signal, potentially yielding important consistency checks
