Abstract
The cascading gravity model was proposed to eliminate instabilities of the original Dvali, Gabadadze, Porrati model by embedding our $4D$ (where $D$ refers to the number of space-time dimensions) Universe into a $5D$ brane, which is itself embedded in a $6D$ bulk. Thus gravity cascades from $6D$ down to $4D$ as we decrease the length scales. We show that it is possible to extend this setup to lower dimensions as well, i.e. there is a self-consistent embedding of a $3D$ brane into a $4D$ brane, which is itself embedded in a $5D$ bulk and so on. This extension fits well into the ``vanishing dimensions" framework in which dimensions open up as we increase the length scales.
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