Constraints of relic gravitational waves by Pulsar Timing Array:
  Forecasts for the FAST and SKA projects
  Measurement of the pulsar timing residuals provides a direct way to detect
relic gravitational waves at the frequency $f\sim 1/{\rm yr}$. 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.
