Abstract
We explore models of intersecting brane worlds with induced gravity terms on codimension-one branes and on their intersection. Maximally symmetric solutions for the branes and the intersection are found. We find new self-accelerating solutions. In a 6D spacetime, the solutions realize the seesaw modification of gravity where the UV scale of the modification to 4D gravity is determined by 6D Planck scale given by ${M}_{6}\ensuremath{\sim}{10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{eV}$ and the IR scale of the modification is determined by ${M}_{6}^{2}/{M}_{4}\ensuremath{\sim}{H}_{0}\ensuremath{\sim}{10}^{\ensuremath{-}42}\text{ }\text{ }\mathrm{GeV}$, where ${H}_{0}$ is the present-day Hubble scale. We find that it is increasingly difficult to construct phenomenologically viable models in higher-dimensional spacetime due to the necessity to have the lower value for the fundamental Planck scale to realize the late time acceleration. It is found that the system also admits self-tuning solutions where the tension at the intersection does not change the geometry of the intersection. The induced gravity terms can avoid the necessity to compactify the extra dimensions. Finally, we discuss the possibility to have ordinary matter at the intersection, without introducing any regularization, using the induced gravity terms.
Highlights
Brane-world models with large distance modification of Einstein gravity are invoked in scenarios that aim to geometrically describe present-day acceleration, without introducing dark energy [1,2,3]
It is important to recognize that the induced gravity terms on the codimension-one branes provide contributions that are similar to the ones that appear in the DGP brane worlds in five dimensions
We find that localized gravity terms on the codimension-one branes induce contributions proportional to M5;i which are again similar to the ones in the DGP models in five dimensions
Summary
Brane-world models with large distance modification of Einstein gravity are invoked in scenarios that aim to geometrically describe present-day acceleration, without introducing dark energy [1,2,3] (for a review see [4]). In the finite volume case, consistency conditions associated to the quantization condition of a background flux which is introduced to compactify the extra-dimensional space are shown to be problematic and the self-tuning mechanism in its simplest form does not work [13] More in general, another delicate feature of codimension-two brane models (both with finite- and infinite-volume) is related to the fact that only the energy-momentum tensor of the form of pure tension can be accommodated on a thin radially symmetric codimension-two brane, to ensure the regularity of the background metric at the brane position [14]. It is interesting to note that induced curvature terms appear quite generically in junction conditions of higher codimension branes when considering natural generalizations of Einstein gravity [15,19] as well as in string theory compactifications [30], orientifold models, and intersecting Dbrane models [31]. A straightforward calculation using the relation between the Ci functions and the induced Hubble parameters leads to the following conditions:
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