从原始核合成、脉冲星计时、laser干涉仪和CMB联系引力波约束：早期宇宙的意义
Relating gravitational wave constraints from primordial nucleosynthesis, pulsar timing, laser interferometers, and the CMB: implications for the early universe
摘要：
我们导出了引力波观测量r和Omega_gw（f）之间的一般主方程。这里r是张量标量比，受宇宙微波背景实验（CMB）的约束; Omega_gw（f）是原始引力波的能谱，例如受脉冲星定时测量、激光干涉仪实验和大爆炸核合成（BBN）的约束。对主方程求导得到倾斜d（ln Omega_gw（f））/d（ln f）的新表达式。r和Omega_gw（f）之间的关系敏感地依赖于早期宇宙的不确定性物理，我们表明，这种不确定性可能被封装（以与模型无关的方式）通过两个量：w_hat（f）和nt_hat（f），其中nt_hat（f）是nt（k）上的某个对数平均值（原始张量谱指数）; w_hat（f）是对w_tilde（a）（视界重返后早期宇宙的有效状态方程）的某个对数平均。这里，有效状态方程参数w_tilde（a）是普通状态方程参数w（a）和体积粘度zeta（a）的组合。因此，通过比较r和Omega_gw（f）上的约束，可以获得[w_hat（f），nt_hat（f）]平面中的（非常紧的）约束。特别是，这是限制（或检测）在BBN之前的早期宇宙中存在“刚性”能量成分（w > 1/3）的最佳方法。最后，虽然我们的分析大多没有假设暴胀，但我们指出，如果CMB实验检测到r的非零值，那么我们将立即获得（作为免费的副产品）在暴胀结束和BBN开始之间的“原始黑暗时代”期间，在数学平均的有效状态方程参数上的新上限w_hat < 0.55。
英文摘要：
We derive a general master equation relating the gravitational-wave observables r and Omega_gw(f). Here r is the tensor-to-scalar ratio, constrained by cosmic-microwave-background (CMB) experiments; and Omega_gw(f) is the energy spectrum of primordial gravitational-waves, constrained e.g. by pulsar-timing measurements, laser-interferometer experiments, and Big Bang Nucleosynthesis (BBN). Differentiating the master equation yields a new expression for the tilt d(ln Omega_gw(f))/d(ln f). The relationship between r and Omega_gw(f) depends sensitively on the uncertain physics of the early universe, and we show that this uncertainty may be encapsulated (in a model-independent way) by two quantities: w_hat(f) and nt_hat(f), where nt_hat(f) is a certain logarithmic average over nt(k) (the primordial tensor spectral index); and w_hat(f) is a certain logarithmic average over w_tilde(a) (the effective equation-of-state in the early universe, after horizon re-entry). Here the effective equation-of-state parameter w_tilde(a) is a combination of the ordinary equation-of-state parameter w(a) and the bulk viscosity zeta(a). Thus, by comparing constraints on r and Omega_gw(f), one can obtain (remarkably tight) constraints in the [w_hat(f), nt_hat(f)] plane. In particular, this is the best way to constrain (or detect) the presence of a ``stiff'' energy component (with w > 1/3) in the early universe, prior to BBN. Finally, although most of our analysis does not assume inflation, we point out that if CMB experiments detect a non-zero value for r, then we will immediately obtain (as a free by-product) a new upper bound w_hat < 0.55 on the logarithmically averaged effective equation-of-state parameter during the ``primordial dark age'' between the end of inflation and the start of BBN.
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