Abstract
We consider localization of gravity in smooth domain wall solutions of gravity coupled to a scalar field with a generic potential in the presence of the Gauss–Bonnet term. We discuss conditions on the scalar potential such that domain wall solutions are non-singular. We point out that the presence of the Gauss–Bonnet term does not allow flat solutions with localized gravity that violate the weak energy condition. We also point out that in the presence of the Gauss–Bonnet term infinite tension flat domain walls violate positivity. In fact, for flat solutions unitarity requires that on the solution the scalar potential be bounded below.
Highlights
In the Brane World scenario the Standard Model gauge and matter fields are assumed to be localized on branes, while gravity lives in a larger dimensional bulk of space–time [1,2,3,4,5,6,7,8,9,10,11,12]
The extra dimensions in such scenarios are non-compact while their volume is finite and fixed in terms of other parameters in the theory such as those in the scalar potential
The expectation values of the scalars descending from the components of the higher dimensional metric corresponding to the extra dimensions are fixed
Summary
In the Brane World scenario the Standard Model gauge and matter fields are assumed to be localized on branes (or an intersection thereof), while gravity lives in a larger dimensional bulk of space–time [1,2,3,4,5,6,7,8,9,10,11,12]. If we truncate the bulk action at any finite higher derivative level, generic higher curvature terms would lead to the appearance of ghosts in the Hilbert space To avoid these difficulties, one might consider adding special “topological” combinations which do not spoil unitarity [17,18]. We can have A 0 subject to the following additional requirement: (A ) β2/λκ In this case gravity is localized as long as A goes to −∞ at y → ±∞ fast enough. The presence of the Gauss–Bonnet term does not allow flat solutions with localized gravity that violate the weak energy condition (that is, the analog of the c-theorem [23])
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