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Using a statistically rigorous analysis method, we place limits on theexistence of an isotropic stochastic gravitational wave background using pulsartiming observations. We consider backgrounds whose characteristic strainspectra may be described as a power-law dependence with frequency. Suchbackgrounds include an astrophysical background produced by coalescingsupermassive black-hole binary systems and cosmological backgrounds due torelic gravitational waves and cosmic strings. Using the best available data, weobtain an upper limit on the energy density per unit logarithmic frequencyinterval of \Omega^{\rm SMBH}_g(1/8yr) h^2 <= 1.9 x 10^{-8} for anastrophysical background which is five times more stringent than the earlierKaspi et al. (1994) limit of 1.1 x 10^{-7}. We also provide limits on abackground due to relic gravitational waves and cosmic strings of \Omega^{\rmrelic}_g(1/8yr) h^2 <= 2.0 x 10^{-8} and \Omega^{\rm cs}_g(1/8yr) h^2 <= 1.9 x10^{-8} respectively. All of the quoted upper limits correspond to a 0.1% falsealarm rate together with a 95% detection rate. We discuss the physicalimplications of these results and highlight the future possibilities of theParkes Pulsar Timing Array project. We find that our current results can 1)constrain the merger rate of supermassive binary black hole systems at high redshift, 2) rule out some relationships between the black hole mass and thegalactic halo mass, 3) constrain the rate of expansion in the inflationary eraand 4) provide an upper bound on the dimensionless tension of a cosmic stringbackground.Comment: Accepted by Ap

Upper Bounds on the Low‐Frequency Stochastic Gravitational Wave Background from Pulsar Timing Observations: Current Limits and Future Prospects