Inflation and large internal dimensions

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 59, Issue 10, 1999, Pages

  Kaloper, Nemanja ^a   Linde, Andrei ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17044430535     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.59.101303     Document Type: Article

References (47)

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42. Our solution (9) can be obtained by directly solving Einstein’s equations in 5D with the 3 brane stress-energy (Formula presented), where (Formula presented) is the generalized surface tension. The (Formula presented) sign is due to our metric signature convention (Formula presented). The general form of the metric (9) is an obvious generalization of the metric obtained in 22. A somewhat nontrivial step is to find a relation between H and (Formula presented). To do so, we use the equations of motion, and find the Ricci tensor on the brane: (Formula presented), where (Formula presented). Since the curvature is singular, by symmetry all one needs to check is the divergence of (Formula presented). The only singularity arises from (Formula presented). Hence (Formula presented), in contrast to 22, where (Formula presented) and (Formula presented). This completes the derivation of our solution (9). The solution for a general case of a (Formula presented) brane in D dimensions is very similar, with (Formula presented). One may also consider a p brane in D dimensions. The stress energy tensor for it is (Formula presented), and the Ricci tensor on the brane is (Formula presented). For the 3 brane in 6D, this gives (Formula presented). In general, for (Formula presented) one has (Formula presented). 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 (Formula presented) and (Formula presented). 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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