The quantum field theory prediction of the cosmological constant is 120 orders of magnitude higher than the observed value. This is known as the cosmological constant problem. Here, we deal with the cosmological constant as a scalar field generated by the reduced extra dimensions, following Kaluza-Klein reduction, in the superstring theory frame, where the vacuum energy is the minimum of this field. We find methods for calculating the cosmological constant, whose value is much lower than those obtained with the current methods of quantum field theory. We conclude that the small cosmological constant value could be explained by the behavior of the mentioned scalar field, and finally we discuss a possible explanation for the observed accelerated expansion of the Universe.
