

8.2 The simplest model
The simplest model is the one in which
in the background, with
. The
regulator brane is assumed to be far enough away that its effects
on the physical brane can be neglected over the timescales of
interest. By Equation (372) it follows that
i.e., the matter on the regulator brane must have fine-tuned and
negative energy density to prevent the regulator brane from moving
in the background. With these assumptions, and further assuming
adiabatic perturbations for the matter, there is only one
independent brane-world parameter, i.e., the parameter measuring
dark radiation fluctuations:
This assumption has a remarkable consequence on large
scales: The Weyl anisotropic stress
terms in the
Sachs-Wolfe formula (321) cancel the entropy
perturbation from dark radiation fluctuations, so that there is no
difference on the largest scales from the standard general
relativity power spectrum. On small scales, beyond the first
acoustic peak, the brane-world corrections are negligible. On
scales up to the first acoustic peak, brane-world effects can be
significant, changing the height and the location of the first
peak. These features are apparent in Figure 12. However, it is not
clear to what extent these features are general brane-world
features (within the low-energy approximation), and to what extent
they are consequences of the simple assumptions imposed on the
background. Further work remains to be done.
A related low-energy approximation, using the
moduli space approximation, has been developed for certain 2-brane
models with bulk scalar field [268
, 37
]. The effective
gravitational action on the physical brane, in the Einstein frame,
is
where
is a coupling constant, and
and
are moduli fields (determined by the
zero-mode of the bulk scalar field and the radion). Figure 13 shows how the CMB
anisotropies are affected by the
-field.

