Constraints on Generalized Inflationary Cosmologies

We consider cosmologies having an inflationary period during which the Robertson-Walker scale factor is an arbitrary function of time satisfying /~ > 0 (not necessarily an exponential). We show that any such inflationary period will produce long-wavelength gravitational waves which can affect present observations of the microwave background. Using present bounds on the quadrupole anisotropy we derive constraints on general inflationary cosmologies. Models with power law inflation (R ~ P') are considered in detail and the maximum reheating temperature is given as a function of p. Finally, predictions for the anisotropy of the microwave background produced by gravitational waves generated by ordinary exponential inflation are presented.