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α=0. In general, for p+3≤D one has R ≤0. This suggests that the branes in a space with more than one uncompactified dimension would not inflate. A particular example is provided by cosmic strings in 4D, for which p =1 and D=4. Unlike domain walls, cosmic strings do not inflate. This result suggests that in order to have inflation on the wall, we need to consider models where at most one dimension remains uncompactified. The class of models proposed in [1] satisfies this condition.
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