6.7 Tensor perturbations

The covariant description of tensor modes on the brane is via the shear, which satisfies the wave equation [304]
[ ( )] ⃗ 2 ¨ ˙ 1- 2 ρ- 2( ˙ℰ ℰ ) ∇ ¯σμν − ¯σμν − 5H ¯σμν − 2Λ + 2κ ρ − 3p − (ρ + 3p)λ ¯σμν − κ ¯πμν + 2H ¯πμν . (353 )
Unlike the density and vector perturbations, there is no closed system on the brane for large scales. The KK anisotropic stress ¯πℰμν is an unavoidable source for tensor modes on the brane. Thus it is necessary to use the 5D metric-based formalism. This is the subject of the next Section 7.


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