 
Summary: Nuclear Physics B264 (1986) 487492
© NorthHolland Publishing Company
GRAVITON PRODUCTION IN INFLATIONARY COSMOLOGY
L.F. ABBOTF' and D.D. HARARI 2
Physics Department, Brandeis Unioersity, Waltham, MA 02254, USA
Received 5 August 1985
We provide a completely quantummechanical derivation of the spectrum of gravitational
waves produced in any inflationary cosmology. The gravitational waves result from a sequence of
Bogoliubov transformations between creation and annihilation operators defined in de Sitter space
and in radiation and matterdominated RobertsonWalker spacetimes. We discuss how the results
depend on the initial state at the beginning of the inflationary period.
The production of gravitational waves in an inflationary cosmology provides an
important constraint on any model of inflation [14]. The Hubble constant during
the de Sitter phase must be less than 1015GeV or else these gravitational waves will
produce unacceptably large anisotropies in the microwave background radiation
[14]. Similar constraints hold for power law or any other form of inflation [4].
The gravitational waves can also affect pulsar timing measurements [5].
The calculation of the spectrum of gravitational waves produced by inflation is
similar to, although simpler than, the calculation for the scalar energydensity
fluctuations [6] which give rise to largescale structure in an inflationary universe.
