Extrinsic curvature effects in brane-world scenarios

Details Extrinsic curvature effects in brane-world scenarios Extrinsic curvature effects in brane-world scenarios

2011-03-16

arxiv.org/abs/1103.3230v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages; v2: typos corrected

Scientific paper

We consider models of bosons on curved 3+1 dimensional space-time embedded in a higher dimensional flat ambient space. We propose to derive (rather than postulate) equations of motions by assuming that a standard Klein-Gordon field on ambient space is restricted to space-time by a strong confining potential. This leads to a modified Klein-Gordon equation on space-time which includes, in addition to the standard terms, a term with a so-called induced potential which depends on intrinsic- and extrinsic curvature of the embedded space-time but not on the details of the confining potential. We compute this induced potential for natural, simple embeddings of Schwarzschild- and Robertson-Walker space-times. We also discuss possible observable implications of our results and, in particular, propose and study an extension of a standard model of cosmological inflation taking into account extrinsic curvature effects. We show that the modified model allows for a solution where the scaling function vanishes like a power law with exponent 0.6830.. at some initial time.

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