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Physics Letters B, 2000

We analyze cosmological equations in the brane world scenario with one extra space-like dimension. We demonstrate that the cosmological equations can be reduced to the usual 4D Friedmann type if the bulk energy-momentum tensor is different from zero. We then generalize these equations to the case of a brane of finite thickness. We also demonstrate that when the bulk energy-momentum tensor is different from zero, the extra space-like dimension can be compactified with a single brane and show that the stability of the radius of compactification implies standard cosmology and vice versa. For a brane of finite thickness, we provide a solution such that the 4D Planck scale is related to the fundamental scale by the thickness of the brane. In this case, compactification of the extra dimension is unnecessary.

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Single-brane cosmological solutions with a stable compact extra dimension

Physical Review D, 2000

We consider 5-dimensional cosmological solutions of a single brane. The correct cosmology on the brane, i.e., governed by the standard 4-dimensional Friedmann equation, and stable compactification of the extra dimension is guaranteed by the existence of a non-vanishing \hat{T}^5_5 which is proportional to the 4-dimensional trace of the energy-momentum tensor. We show that this component of the energy-momentum tensor arises from the backreaction of the dilaton coupling to the brane. The same positive features are exhibited in solutions found in the presence of non-vanishing cosmological constants both on the brane (\Lambda_{br}) and in the bulk (\Lambda_B). Moreover, the restoration of the Friedmann equation, with the correct sign, takes place for both signs of LambdaB\Lambda_BLambdaB so long as the sign of Lambdabr\Lambda_{br}Lambdabr is opposite LambdaB\Lambda_BLambdaB in order to cancel the energy densities of the two cosmological constants. We further extend our single-brane thin-wall solution to allow a brane with finite thickness.

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