Searching for gravitational-wave bursts from cosmic string cusps with the Parkes Pulsar Timing Array third data release

Pulsar timing arrays (PTAs) are designed to detect nanohertz-frequency gravitational waves (GWs). Since GWs are anticipated from cosmic strings, PTAs offer a viable approach to testing their existence. We present the results of the first Bayesian search for gravitational-wave bursts from cosmic string cusps (GWCS) using the third PPTA data release for 30 millisecond pulsars. In this data collection, we find no evidence for GWCS signals. We compare a model with a GWCS signal to one with only noise, including a common spatially uncorrelated red noise (CURN), and find that our data is more consistent with the noise-only model.We then establish upper limits on the strain amplitude of GWCS at the pulsar term, based on the analysis of 30 millisecond pulsars, after finding no compelling evidence. We find the addition of a CURN with different spectral indices into the noise model has a negligible impact on the upper limits. And the upper limit range of the amplitude of the pulsar-term GWCS is concentrated between 10^{-12} and 10^{-11}. Finally, we set upper limits on the amplitude of GWCS events, parametrized by width and event epoch, for a single pulsar PSR J1857+0943. Moreover, we derive upper limit on the cosmic string tension as a function of burst width and compare it with previous results.