Accelerating internal dimensions and nonzero positive cosmological constant

Abstract

We present a new scenario for the moduli stabilization with a very small but nonzero positive cosmological constant λ. In this scenario the complex structure moduli are still stabilized by the three-form fluxes as in the usual flux compactifications, but the Kähler modulus is not fixed by the KKLT scenario. In our case the scale factor (or the Kähler modulus) of the internal dimensions is basically allowed to change with time. But at the supergravity level it is fixed by a set of dynamical (plus constraint) equations defined on the 4D spacetime, not by the nonperturbative corrections of KKLT. Also at the supergravity level it is shown that λ is fine-tuned to zero, λ=0, by the same set of 4D equations. This result changes once we admit α′-corrections of the string theory. The fine-tuning λ=0 changes into λ=23Q, where Q is a constant representing quantum corrections of the brane and 6D action defined on the internal dimensions and its value is determined by the α′-corrections. It is also shown that this nonzero λ must be positive and at the same time the internal dimensions must evolve with time almost at the same rate as the external dimensions in the case of nonzero λ.