Constraint on the early Universe by relic gravitational waves: From pulsar timing observations

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Recent pulsar timing observations by the Parkers Pulsar Timing Array and European Pulsar Timing Array teams obtained the constraint on the relic gravitational waves at the frequency f*=1/ yr, which provides the opportunity to constrain H*, the Hubble parameter when these waves crossed the horizon during inflation. In this paper, we investigate this constraint by considering the general scenario for the early Universe: we assume that the effective (average) equation-of-state w before the big bang nucleosynthesis stage is a free parameter. In the standard hot big-bang scenario with w=1/3, we find that the current PPTA result follows a bound H*≤ 1.15×10⁻¹, and the EPTA result follows H*≤ 6.92×10⁻². We also find that these bounds become much tighter in the nonstandard scenarios with w>1/3. When w=1, the bounds become H*≤5.89×10⁻³ for the current PPTA and H*≤3.39×10⁻³ for the current EPTA. In contrast, in the nonstandard scenario with w=0, the bound becomes H*≤7.76 for the current PPTA.