Abstract
We consider the static domain wall braneworld scenario constructed from the Palatini formalism $f(\mathcal{R})$ theory. We check the self-consistency under scalar perturbations. By using the scalar-tensor formalism we avoid dealing with the higher-order equations. We develop the techniques to deal with the coupled system. We show that under some conditions, the scalar perturbation simply oscillates with time, which guarantees the stability. We also discuss the localization condition of the scalar mode by analyzing the effective potential and the fifth dimensional profile of the scalar mode. We apply these results to an explicit example, and show that only some of the solutions allow for stable scalar perturbations. These stable solutions also give nonlocalizable massless mode. This is important for reproducing a viable four-dimensional gravity.
Highlights
AND MOTIVATIONSThe idea that extra spatial dimensions may exist [1,2,3] has opened up a new gate towards new physics beyond the standard model of particle physics and of cosmology
We consider the static domain wall braneworld scenario constructed from the Palatini formalism fðRÞ theory
We show that the formalism of fðRÞ should be restricted to ensure the stability and the nonlocalization of the massless scalar mode
Summary
The idea that extra spatial dimensions may exist [1,2,3] has opened up a new gate towards new physics beyond the standard model of particle physics and of cosmology. In the previous braneworld models considered in other gravity theories [36,37,38,39,40], the warp factor decays exponentially at the boundaries of the fifth dimension This is because the warp factor is related to the localization condition of the massless graviton. The warp factor in Palatini fðRÞ theory allows for both of the decaying and growing solutions, and they all give the localizable massless graviton [24] This may provide some new mechanisms to localize standard model particle fields. It is interesting to note that the domain wall brane in general relativity with a scalar field always gives a nonlocalizable scalar mode, as long as the background geometry is asymptotically AdS5, which is a very weak restriction Such a theory allows for a wide class of models and there are few constraints on the theory.
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