Dilaton dynamics in (A) dS₅×S⁵

We investigate a stabilization of extra dimensions in a ten-dimensional Kaluza-Klein theory, and type IIB supergravity. We assume (A)dS ₅×S⁵ compactification, and calculate quantum effects to find an effective potential for the radius of internal space. The effective potential has a minimum, and if the universe is created on the top of the potential hill, the universe evolves from dS₅ to AdS₅ after exponential expansion. The internal space S⁵ stays small and its radius becomes constant. Our model in type IIB supergravity contains the 4-form gauge field with a classical vacuum expectation value, which is the role of a ten-dimensional cosmological constant. If the universe evolves into anti-de Sitter, the five-dimensional Randall-Sundrum setup with a stabilized dilaton is obtained from the type IIB supergravity model.