Signals from millisecond pulsars, being exceptionally accurate clocks, are sensitive to a cosmic background of gravitational waves1-3. Present measurements imply that the the energy density in such waves in an octave bandwidth near 10-7 Hz must be ≲10-3 of the closure density2. Gravitational waves of these frequencies may be produced by a variety of sources of astrophysical or cosmological interest3,4. I investigate here the sensitivity of a millisecond pulsar timing signal to the background of gravitational waves expected from an inflationary phase of expansion during the early Universe5. The spectrum of such waves, which is flat, extends up to and beyond periods of the order of the present Hubble time. As such, their amplitude can be constrained by measurements of the present quadrupole anisotropy of the black-body background6-8. I demonstrate here that the bound on inflation derived from millisecond pulsar timing measurements2 is, at present, much weaker than this bound. However, the millisecond pulsar bound should, with new technology and the possible discovery of new pulsars, improve dramatically and it may eventually surpass the present quadrupole bound. It is in principle sensitive to the shape of the gravitational wave spectrum and can thus serve as a stronger test of inflationary predictions.9-11 A positive millisecond pulsar signal can also be used to measure photon reheating processes in the early Universe below temperatures of the order of 100 MeV.
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