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Partial reduction is a Randall-Sundrum reduction for only part of the AdSregion between finite tension brane and zero tension brane. This is interestingin AdS/BCFT where the AdS bulk contains a defect brane. We employ partialreduction for a AdS bulk with a brane evolving as a $2d$Friedmann-Robertson-Walker (FRW) cosmology and demonstrate the equivalencebetween defect extremal surface and island formula for a large subregion finegrained entropy in boundary CFT. We then move to higher dimensions anddemonstrate the existence of $4d$ massless graviton on AdS$_4$ brane in partialreduction. We also propose a partial reduction for a $4d$ FRW cosmology atdefect brane and obtain the Newton constant by computing boundary entropy.

Partial Reduction and Cosmology at Defect Brane