Cosmology with an extremely light scalar field

A theory with a vanishing cosmological constant can have a nonzero effective cosmological constant of cosmological significance if the theory has a scalar field with a mass m of the order of the inverse age of the Universe (tau/similar to/10/sup 33/ eV/sup -1/) provided the field has a nonzero but evolving expectation value. We discuss the cosmological consequences of scalar fields with masses mapprox. <10/sup -28/ eV. The effect on the age of the Universe and on the growth of density perturbations is discussed in detail. For small masses (mapprox. <tau/sup -1//similar to/10/sup -33/ eV) the Universe behaves precisely as if a cosmological constant were present. For masses several orders of magnitude greater than tau/sup -1/ for which phi has made several oscillations only density perturbations on scales greater than m/sup -1/ grow significantly