Self-tuning solution of the cosmological constant problem with antisymmetric tensor field

We present a self-tuning solution of the cosmological constant problem with one extra dimension which is curved with a warp factor. To separate out th e extra dimension and to have a self-tuning solution, a three index antisym metric tensor field is introduced with the 1/H-2 term in the Lagrangian. Th e standard model fields are located at the y = 0 brane. The existence [1] o f the self-tuning solution (which results without any fine tuning among par ameters in the Lagrangian) is crucial to obtain a vanishing cosmological co nstant in a 4D effective theory. The de-Sitter and anti-de-Sitter space sol utions are possible. The de-Sitter space solutions have horizons. Restricti ng to the spaces which contain the y = 0 brane, the vanishing cosmological constant is chosen in the most probable universe. For this interpretation t o be valid, the existence of the self-tuning solution is crucial in view of the phase transitions. In this paper, we show explicitly a solution in cas e the brane tension shifts from one to another value. We also discuss the c ase with the H-2 term which leads to one-fine-tuning solutions at most. (C) 2001 Published by Elsevier Science B.V.