Graviton Kaluza Klein modes in non-flat branes with stabilised modulus

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We consider a generalised two brane Randall Sundrum model where the branes are endowed with non-zero cosmological constant. In this scenario, we re-examine the modulus stabilisation mechanism and the nature of Kaluza Klein (KK) graviton modes. Our result reveals that while the KK mode graviton masses may change significantly with brane cosmological constant, the Goldberger-Wise stabilisation mechanism, which assumes negligible backreaction on the background metric, continues to hold even when the branes have large cosmological constant. The possibility of having a global minimum for the modulus is also discussed.