For the CMB anisotropies, one needs to consider a multi-component source. Linearizing the general nonlinear expressions for the total effective energy-momentum tensor, we obtain
The perturbation equations in the previous Section 7 form the basis for an analysis of scalar and tensor CMB anisotropies in the brane-world. The full system of equations on the brane, including the Boltzmann equation for photons, has been given for scalar  and tensor  perturbations. But the systems are not closed, as discussed above, because of the presence of the KK anisotropic stress , which acts a source term.
In the tight-coupling radiation era, the scalar perturbation equations may be decoupled to give an equation for the gravitational potential , defined by the electric part of the brane Weyl tensor (not to be confused with ): :
The formalism and machinery are ready to compute the temperature and polarization anisotropies in brane-world cosmology, once a solution, or at least an approximation, is given for . The resulting power spectra will reveal the nature of the brane-world imprint on CMB anisotropies, and would in principle provide a means of constraining or possibly falsifying the brane-world models. Once this is achieved, the implications for the fundamental underlying theory, i.e., M theory, would need to be explored.
However, the first step required is the solution for . This solution will be of the form given in Equation (249). Once and are determined or estimated, the numerical integration in Equation (249) can in principle be incorporated into a modified version of a CMB numerical code. The full solution in this form represents a formidable problem, and one is led to look for approximations.
This work is licensed under a Creative Commons License.