Is pulsar timing a hopeful tool for detection of relic gravitational waves by using GW150914 data?

The inflation stage has a behaviour as power law expansion like S(η) ∝ η^1+β where β constrained on the 1 + β < 0. If the inflation were preceded by a radiation era, then there would be thermal spectrum of relic gravitational waves at the time of inflation. Based on this idea we find new upper bound on β by comparison the thermal spectrum with strain sensitivity of single pulsar timing. Also we show that sensitivity curve of single pulsar timing may be hopeful tool for detection of the spectrum in usual and thermal case by using the GW150914 data. (orig.)