A small cosmological constant from warped compactification with branes

We present a possible explanation for the smallness of the observed cosmolo gical constant using a variant of the Randall-Sundrum(RS)-Goldberger-Wise p aradigm for a warped extra dimension. In contrast to RS. we imagine that we are living on the positive tension Planck brane. or on a zero-tension TeV brane. In our model there are two solutions for the scalar field in the bul k and the corresponding brane separations, one of which is tuned to have ze ro cosmological constant. We show that in the other solution, which is a fa lse vacuum state, the 4-D cosmological constant can be naturally small, due to exponential suppression by the warp factor. The radion is in the milli- eV mass range, and if we live on a TeV brane its couplings are large enough that it can measurably alter the gravitational force at submillimeter dist ances. In this case the Kaluza-Klein excitations of the graviton can also c ontribute to submillimeter deviations from Newtonian gravity, and we have i n addition the collider phenomenology of the usual TeV-scale radion. (C) 20 01 Published by Elsevier Science B.V.