Dark energy as an off-shell tachyon background in four-dimensional strings

We consider a time-dependent bosonic string in graviton, dilaton and tachyon backgrounds, for which it was already shown that conformal invariance is respected to all orders in α′ and in any space-time dimension. Assuming that the tachyon is off-shell, we show in this note that the specific time-homogeneity of the corresponding space-time effective action leads to a power-law expanding Universe, that can be interpreted as dark energy. We arrive at this result without requiring the knowledge of the structure of the string effective action, which is not known to all orders in α′. Moreover, in our approach, the background configurations are consistent in a four-dimensional space-time, without any need for extra dimensions.