Relaxing the cosmological moduli problem

Typically the moduli fields acquire mass $m_{\phi }^2=\pm C^2{H}^2$ in the early universe, which shifts the position of the minimum of their effective potential and leads to an excessively large energy density of the oscillating moduli fields at the later stages of the evolution of the universe. This constitutes the cosmological moduli problem, or Polonyi field problem. We show that the cosmological moduli problem can be solved or at least significantly relaxed in the theories in which $C\gg 1$, as well as in some models with $C\ll 1$.