Measurement of the pulsar timing residuals provides a direct way to detect relic gravitational waves at the frequency f \sim 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 ( PTAs ) .
We find that Five-hundred-meter Aperture Spherical radio Telescope ( FAST ) in China and the planned Square Kilometer Array ( SKA ) projects have the fairly strong abilities to test the phantom-like inflationary models .
If r = 0.1 , FAST could give the constraint on the spectral index n _ { t } < 0.56 , and SKA gives n _ { t } < 0.32 .
While an observation with the total time T = 20 yr , the pulsar noise level \sigma _ { w } = 30 ns and the monitored pulsar number n = 200 , could even constrain n _ { t } < 0.07 .
These are much tighter than those inferred from the current results of Parkers Pulsar Timing Array ( PPTA ) , European Pulsar Timing Array ( EPTA ) and North American Nanohertz Observatory for Gravitational waves ( NANOGrav ) .
Especially , by studying the effects of various observational factors on the sensitivities of PTAs , we found that compared with \sigma _ { w } and n , the total observation time T has the most significant effect .