Figures 7-10
Figure 7
Uncovering the Potential Envelope. The potential envelope
is obscured by diffusion damping. By numerically removing the
damping, one sees that the intrinsic fluctuations follow the
analytic estimates of ${\cal P}_\ell$ reasonably well. By multiplying
by the numerically-calibrated damping function ${\cal D}_\ell^2$, one
recovers the form of the full calculation even at very small angles.
The model here is standard CDM.
Figure 8
Constraining $\Omega_0$ with the damping tail.
By measuring
the anisotropy power in at some scale $\ell$ in the damping tail
(here averaged over 10\% in $\ell$) and comparing it to a reference
scale (here $\ell=2$), one determines the ratio of intrinsic
powers ${\cal P}_\ell/{\cal P}_2$
before damping necessary to reproduce the observation
(here $\Omega_0=1$ in standard CDM).
Since this is a strong function of the assumed $\Omega_0$, only order
of magnitude knowledge of the model-dependent intrinsic power
is needed (e.g. square, estimated from Eq.~(32))
to reject values of $\Omega_0$. Multiple measurements
in the damping tail largely removes this ambiguity (curve intersection).
For simplicity, we have fixed $h=0.5$, $\Omega_bh^2=0.0125$ and
$\Omega_\Lambda=0$.
Figure 9
Reionization damping in standard CDM. Damping described by the
envelope ${\cal R}_\ell$ is the main effect of late reionization in CDM
type models. Hence employing either the numerical calibration of
${\cal R}_\ell$ and the fit to it from Eq.~(24) to filter the results of a
standard recombination (SR, no reionization) calculation approximate the
full calculation to better than 1\% in power. The scatter at low $\ell$
is a numerical artifact from finite sampling of the $C_\ell$ integral in
$k$-space (see Eq.~(4)).
Figure 10
Reionization and the Doppler Effect. For early ionization,
the Doppler effect due to the relative electron-photon velocity can
regenerate fluctuations around the horizon scale at the last scattering
epoch. By comparing the standard recombination (SR) result filtered
by reionization damping ${\cal R}_\ell^2$ to the full calculation,
we can uncover such effects.