论文标题
从宇宙微波背景的原始重力波的限制
Constraints on primordial gravitational waves from the Cosmic Microwave Background
论文作者
论文摘要
对原始引力波的搜索已导致各种来源的频率范围很大。标准宇宙微波背景（CMB）技术是用张量与尺度比率，$ r $和频谱索引，$ n _ {\ rm t} $来参数张量的功率谱，并使用温度和极化电源的测量值来约束这些功能。另一种适用于重组时宇宙学视野内部模式的方法，使用短波近似，在该近似值下，重力波的行为作为有效的中微子物种。在本文中，我们对重力波的能量密度给出了模型无关的CMB约束，对于整个可观察的频率，$ω__\ textrm {gw} h^2 $。在大尺度上，$ f \ lyssim 10^{ - 16} \，\ text {hz} $，我们重建对数频率箱中的初始张量功率谱，从而找到接近地平线的量表的最大敏感性。在小尺度上，$ f \ gtrsim10^{ - 15} \，\ mbox {hz} $，我们使用短波近似值，查找$ω__\ textrm {gw} h^2 <1.7 \ 1.7 \ times10^{ - 6} $ diabication初始条件和$ω__\ textrm \ 2.2 \ times10^{ - 7} $用于均质初始条件（均为$2σ$上限）。对于重组时接近地平线大小的量表，我们使用二阶扰动理论来计算重力波的背部反应，找到$ω__\ textrm {gw} h^2 <8.4 \ 8.4 \ times10^{ - 7} $ \ times10^{ - 7} $包括中微子各向异性压力。这些约束对于$ 10^{ - 15} \，\ text {hz} \ gtrsim f \ gtrsim 3 \ times 10^{ - 16} \，\ text {hz} $有效。
Searches for primordial gravitational waves have resulted in constraints in a large frequency range from a variety of sources. The standard Cosmic Microwave Background (CMB) technique is to parameterise the tensor power spectrum in terms of the tensor-to-scalar ratio, $r$, and spectral index, $n_{\rm t}$, and constrain these using measurements of the temperature and polarization power spectra. Another method, applicable to modes well inside the cosmological horizon at recombination, uses the shortwave approximation, under which gravitational waves behave as an effective neutrino species. In this paper we give model-independent CMB constraints on the energy density of gravitational waves, $Ω_\textrm{gw} h^2$, for the entire range of observable frequencies. On large scales, $f \lesssim 10^{-16}\, \text{Hz}$, we reconstruct the initial tensor power spectrum in logarithmic frequency bins, finding maximal sensitivity for scales close to the horizon size at recombination. On small scales, $f \gtrsim10^{-15}\,\mbox{Hz}$, we use the shortwave approximation, finding $Ω_\textrm{gw} h^2 < 1.7 \times10^{-6}$ for adiabatic initial conditions and $Ω_\textrm{gw} h^2 < 2.9 \times10^{-7}$ for homogeneous initial conditions (both $2σ$ upper limits). For scales close to the horizon size at recombination, we use second-order perturbation theory to calculate the back-reaction from gravitational waves, finding $Ω_\textrm{gw} h^2 < 8.4 \times10^{-7}$, in the absence of neutrino anisotropic stress and $Ω_\textrm{gw} h^2 < 8.6 \times10^{-7}$ when including neutrino anisotropic stress. These constraints are valid for $ 10^{-15}\, \text{Hz} \gtrsim f \gtrsim 3 \times 10^{-16}\, \text{Hz}$.
