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Recently, it was found by Greene and Levin that the Casimir energy of certain combinations of massless and massive fields in space with extra dimensions play a crucial role in the accelerated expansion of the late-time universe and therefore it could serve as a candidate for the dark energy. It also provides a mechanism in stabilizing the volume moduli of extra dimensions. However, the shape moduli of the extra dimensions were never taken into account in the previous work. We therefore study the stabilization mechanism for both volume and shape moduli due to the Casimir energy in M 1+3 × T 2 . The result of our study shows that the previously known local minimum is a saddle point. It is unstable to the perturbations in the direction of the shape moduli. The new stable local minima stabilizes all the moduli and drives the accelerating expansion of the universe. The cosmological dynamics both in the bulk and the radion pictures are derived and simulated. The equations of state for the Casimir energy in a general torus are derived. Shear viscosity in extra dimensions induced by the Casimir density in the late times is identified and calculated, it is found to be proportional to the Hubble constant.

Abstract:We consider the inhomogeneous decay of an unstable D-brane of bosonic string theory in a linear dilaton background in a light-cone frame. At the lowest level, the dynamical equation that describes this process is a generalisation (that includes nonlocality and time delay) of a reaction-diffusion equation studied by Fisher (and others). We argue that the equation of motion of the cubic open string field theory is satisfied at least to the second order when we start with this 'Fisher deformation', a marginal operator which has a simple pole term in its OPE. We also compute the one-point functions of closed string operators on the disc in the presence of this deformation.

The dynamics (in light-cone time) of the tachyon on an unstable brane in the background of a dilaton linear along a null coordinate is a non-local reaction-diffusion type equation, which admits a travelling front solution. We analyze the (in-)stability of this solution using linearized perturbation theory. We find that the front solution obtained in singular perturbation method is stable. However, these inhomogenous solutions (unlike the homogenous solution) also have Lyapunov exponents corresponding to unstable modes around the (meta-)stable vacuum.

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