Dilaton dynamics in [Formula Presented]

We investigate a stabilization of extra dimensions in a ten-dimensional Kaluza-Klein theory and type IIB supergravity. We assume [Formula Presented] 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 [Formula Presented] to [Formula Presented] after exponential expansion. The internal space [Formula Presented] 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.