Constraints of relic gravitational waves by pulsar timing arrays: Forecasts for the FAST and SKA projects

Measurement of pulsar timing residuals provides a direct way to detect relic gravitational waves at the frequency f similar to 1/yr. In this paper, we investigate the constraints on the inflationary parameters, the tensor-to-scalar ratio r, and the tensor spectral index n(t), by the current and future pulsar timing arrays. We find that the Five-hundred-meter Aperture Spherical Radio Telescope in China and the planned Square Kilometre Array projects have fairly strong abilities to test the phantomlike inflationary models. If r = 0.1, then Five-hundred-meter Aperture Spherical Radio Telescope could give the constraint on the spectral index n(t) < 0.56 and Square Kilometre Array could give n(t) < 0.32, while an observation with total time T = 20 yr, pulsar noise level sigma(w) = 30 ns, and monitored pulsar number n = 200 could even constrain n(t) < 0.07. These are much tighter than those inferred from the current results of the Parkes Pulsar Timing Array, European Pulsar Timing Array, and North American Nanohertz Observatory for Gravitational Waves. By studying the effects of various observational factors on the sensitivities of pulsar timing arrays, we find that compared with sigma(w) and n, the total observation time T has the most significant effect.