Relic gravitational waves ( RGWs ) , a background originated during inflation , would give imprints on the pulsar timing residuals .
This makes RGWs be one of important sources for detection using the method of pulsar timing .
In this paper , we discuss the effects of RGWs on the single pulsar timing , and give quantitively the timing residuals caused by RGWs with different model parameters .
In principle , if the RGWs are strong enough today , they can be detected by timing a single millisecond pulsar with high precision after the intrinsic red noise in pulsar timing residuals were understood , even though observing simultaneously multiple millisecond pulsars is a more powerful technique in extracting gravitational wave signals .
We corrected the normalization of RGWs using observations of the cosmic microwave background ( CMB ) , which leads to the amplitudes of RGWs being reduced by two orders of magnitude or so compared to our previous works .
We made new constraints on RGWs using the recent observations from the Parkes Pulsar Timing Array , employing the tensor-to-scalar ratio r = 0.2 due to the tensor-type polarization observations of CMB by BICEP2 as a referenced value even though it has been denied .
Moreover , the constraints on RGWs from CMB and BBN ( Big Bang nucleosynthesis ) will also be discussed for comparison .