论文标题
通过密度扰动的重力波光谱的变形
Deformation of the gravitational wave spectrum by density perturbations
论文作者
论文摘要
我们研究了原始标量曲率扰动对宇宙距离上重力波的传播的影响。我们指出，这种曲率扰动通过（综合的）sachs-wolfe效应变形了原始起源重力波的任何随机背景的各向同性光谱。计算通过标态曲率扰动以线性诱导的线性诱导的传播引力波的幅度和频率的变化，我们表明，引力波谱的每个频率bin的所得变形通过线性偏见的高斯与方差$σ^2 \ simeq \ simeq \ simeq \ simeq \ sem proginal interial of in n in pro s in c \ s i p $ c^2 $ r riassian riase shemian r。 $δ_ {\ Mathcal r}^2（k）$表示原始曲率扰动的幅度。线性偏置编码重力波频率和振幅引起的变化之间的相关性。考虑到原始黑洞和引力波搜索的$δ_ {\ Mathcal r}^2 $的最新界限，我们证明所得$ {\ Mathcal O}（σ）$变形对于极高的峰值引力波光谱可能是重要的。我们进一步提供了广泛光谱的数量级估计，净失真为$ {\ MATHCAL O}（σ^2）$。
We study the effect of primordial scalar curvature perturbations on the propagation of gravitational waves over cosmic distances. We point out that such curvature perturbations deform the isotropic spectrum of any stochastic background of gravitational waves of primordial origin through the (integrated) Sachs-Wolfe effect. Computing the changes in the amplitude and frequency of the propagating gravitational wave induced at linear order by scalar curvature perturbations, we show that the resulting deformation of each frequency bin of the gravitational wave spectrum is described by a linearly biased Gaussian with the variance $σ^2 \simeq \int d\ln k Δ_{\mathcal R}^2$, where $Δ_{\mathcal R}^2(k)$ denotes the amplitude of the primordial curvature perturbations. The linear bias encodes the correlations between the changes induced in the frequency and amplitude of the gravitational waves. Taking into account the latest bounds on $Δ_{\mathcal R}^2$ from primordial black hole and gravitational wave searches, we demonstrate that the resulting ${\mathcal O}(σ)$ deformation can be significant for extremely peaked gravitational wave spectra. We further provide an order of magnitude estimate for broad spectra, for which the net distortion is ${\mathcal O}(σ^2)$.
