‘‘Isothermal’’ density perturbations in an axion-dominated inflationary universe

In inflationary models of the Universe which are axion dominated both adiabatic and isothermal density perturbations arise. We point out that the isothermal perturbations can be more important than the adiabatic perturbations and discuss a model for which this is the case. With isothermal perturbations the spectrum of density perturbations when structure formation begins is flatter and we briefly discuss the implications of this fact. That the amplitude of isothermal fluctuations not be too large provides yet another constraint on models of inflation.