In string or $M$ theory with a large compactification radius, some axionlike moduli can be much lighter than the gravitino. Generic moduli in gauge-mediated supersymmetry breaking models also have a mass far below the weak scale. Motivated by these, we examine the cosmological implications of light moduli for the mass range from the weak scale to an extremely small scale of $\mathcal{O}{(10\mathrm{}}^{-26})\hspace{0.5em}\mathrm{eV},$ and obtain an upper bound on the initial moduli misalignment for both cases with and without late entropy production.

• Received 10 February 1998

DOI:https://doi.org/10.1103/PhysRevD.58.046003