Limits from the timing of pulsars on the cosmic gravitational wave background

We calculate how a stochastic background of gravitational waves might contribute to the ‘timing noise’ of pulsars. The published timing data, extending over a timespan T ≲ 10 yr, already provide a limit Ω_g ≲ 10⁻³ on the fraction of the critical cosmological density contributed by waves with periods of a few years; less sensitive limits can also be set for waves of shorter periods. Further analysis of existing data could tighten these limits; they will also improve as the time-base T lengthens. A genuine contribution from background gravitational waves could be distinguished from irregularities intrinsic to the pulsars by searching for correlations between the ‘timing noise’ of different pulsars. The timing data set poor limits to backgrounds with periods ≫ T, because such waves would merely give a contribution to $$\dot P$$ indistinguishable from the effect of intrinsic spin-down, which is much larger and cannot be predicted a priori. However, the orbital period of the binary pulsar provides a ‘clock’ whose intrinsic secular behaviour can already be predicted, on the basis of general relativity, with an accuracy ∼ 10⁻¹¹ yr⁻¹. Searches for disparities between the predicted and measured changes in the orbit could, within a few years, probe the gravitational wave background at periods up to ∼ 10⁴ yr with a sensitivity corresponding to $$\Omega_g\simeq10^{-4}$$.