Exotic baryon and radiation content. (a)
The sound horizon which forms the
basis of the peak-spacing test is independent of $\Omega_b h^2$ for
values near BBN or lower, whereas the damping tail is
insensitive to high $\Omega_b h^2$. In either limit a robust
test exists. The ratio of tail to peak-spacing $\ell_D/\ell_A$
can detect an exotic baryon content. (b)
Changing the radiation content, e.g.~by altering the number of
relativistic neutrinos $N_\nu$, affects the expansion rate and thus
the two physical scales weakly. Cases extreme enough to
affect the scales significantly can also be
distinguished by $\ell_D/\ell_A$.
Exotic ionization history ($\Omega_0h^2=0.25, \Omega_bh^2=0.0125$).
We show the damping and peak-separation scales in a model with
instantaneous recombination at $z_*$. For a gradual recombination,
a lower $\ell_D/\ell_A$ will always result.
The diffusion scale at last scattering by definition approaches the sound
horizon in the limit that no recombination (NR) occurred.
Assuming instantaneous recombination, the ratio $\ell_D/\ell_A$
to the number of observable peaks and can be used to discriminate against
exotic ionization histories.