Cosmological Constant Probing Shape Moduli through Large Extra Dimensions

We consider compactification of extra dimensions and numerically calculate Casimir energy which is provided by the mass of Kaluza-Klein modes. For the extra space we consider a torus with shape moduli and show that the corresponding vacuum energy is represented as a function of the moduli parameter of the extra dimensions. By assuming that the Casimir energy may be identified with cosmological constant, we evaluate the size of extra dimensions in terms of the recent data given by the WMAP observation. We suggest that the observed cosmological constant may probe the shape moduli of the extra space by the study of the Casimir energy of the compactified extra dimensions.