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

Abstract

Using a statistically rigorous analysis method, we place limits on the existence of an isotropic stochastic gravitational wave background using pulsar timing observations. We consider backgrounds whose characteristic strain spectra may be described as a power-law dependence with frequency. Such backgrounds include an astrophysical background produced by coalescing supermassive black-hole binary systems and cosmological backgrounds due to relic gravitational waves and cosmic strings. Using the best available data, we obtain an upper limit on the energy density per unit logarithmic frequency interval of SMBH g 1/(8 yr) ½ h 2 1:9 ; 10 À8 for an astrophysical background that is 5 times more stringent than the earlier limit of 1:1 ; 10 À7 found by Kaspi and colleagues. We also provide limits on a background due to relic gravitational waves and cosmic strings of relic g 1/(8 yr) ½ h 2 2:0 ; 10 À8 and cs g 1/(8 yr)½ h 2 1:9 ; 10 À8 , respectively. All of the quoted upper limits correspond to a 0.1% false alarm rate together with a 95% detection rate. We discuss the physical implications of these results and highlight the future possibilities of the Parkes 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 the galactic halo mass, (3) constrain the rate of expansion in the inflationary era, and (4) provide an upper bound on the dimensionless tension of a cosmic string background.

Sources of Gravitational Waves: Theory and Observations

“…The results have started to exclude regions of the parameter space of expected signals from cosmic (super)strings [502,504,505], and have constrained the equation of state of the Universe during the dark age [502,506]. Moreover, pulsar timing observations have set physically meaningful upper limits for the supermassive BH binary background (Ω GW < 1.3 × 10 −9 at 2.8 nHz) [507] and cosmic (super)strings [508].…”

Blue-tilted tensor spectrum and thermal history of the Universe

“…The degree of the suppression depends on the amount of the entropy produced, which is characterized by the quantity F defined in Eq. (19). The frequency range of the suppression depends on the temperature of the Universe at the end of the second reheating T σ .…”

Lumps in the throat

“…This will put an upper bound on Gµ, the dimensionless number corresponding to cosmic string tension. An even stronger bound may come from recent studies on pulsar timing [50], which can give the upper bound Gµ ≤ 1.5 × 10 −8 . This is within the bound obtained in warped brane-antibrane inflation models [51].…”