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 [38, 268]. The effective gravitational action on the physical brane, in the Einstein frame, is
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