 
Summary: Nuclear Physics B244 (1984) 541548
© NorthHolland Publishing Company
CONSTRAINTS ON GENERALIZED INFLATIONARY COSMOLOGIES
L.F. ABBO'FI"m
Physics Department, Brandeis University, Waltham, MA 02254, USA
Mark B. WISE2
California Institute of Technology, Pasadena, CA 91125, USA
Received 27 March 1984
We consider cosmologies having an inflationary period during which the RobertsonWalker
scale factor is an arbitrary function of time satisfying /~> 0 (not necessarily an exponential). We
show that any such inflationary period will produce longwavelength 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.
1. Introduction
The homogeneity and spatial flatness of the present universe strongly suggest that
some time in the past a period of inflationary expansion occurred [I]. In the usual
inflationary cosmology [1], the RobertsonWalker scale factor grows exponentially
