论文标题
量化双光谱II的红移空间变形：在二阶扰动下引起的非高斯性
Quantifying the Redshift Space Distortion of the Bispectrum II: Induced Non-Gaussianity at Second Order Perturbation
论文作者
论文摘要
红移空间BISPECTRUM $ B^s（\ MATHBF {K_1}，\ MATHBF {K_2}，\ MATHBF {K_3}）$的Anisotrpy，其中包含大量的宇宙学信息，使用大量的宇宙学信息，使用多极点$ \ bar {b}^m _ _ _ _ \ bar）完全量化$ k_1 $，最大的长度和$（μ，t）$分别量化了三角形$（\ Mathbf {k_1}，\ Mathbf {k_2}，\ Mathbf {k_3}）$的大小和形状。我们在二阶扰动理论上介绍了所有预测为非零（$ \ ell \ le 8，m \ le 6 $）的分析表达式。多物也取决于$β_1，b_1 $和$γ_2$，该$分别量化了线性红移变形参数，线性偏置和二次偏置。考虑到所有可能形状的三角形，我们分析了所有具有$ k_1 = 0.2 \，{\ rm mpc}^{ - 1} { - 1}的形状依赖性，β_1= 1，b_1 = 1 $和$γ_2= 0 $固定。单极$ \ bar {b}^0_0 $，到处都是正面的，对于等边三角形而言是最小的。 $ \ bar {b} _0^0 $增加对线性三角形，对于接近挤压极限的线性三角形最大。 $ \ bar {b}^0_ {2} $和$ \ bar {b}^0_4 $都类似于$ \ bar {b}^0_0 $，但是quadrupole $ \ bar {b}^0_2 $超过$ \ bar {b}^0_0 $，而不是重要的范围。另一个多尔斯（其中许多变为负）的大小小于$ \ bar {b}^0_0 $。在大多数情况下，最大值或最小值或两者都非常接近挤压极限。 $ \ mid \ bar {b}^m _ {\ ell} \中$在增加$ \ ell $或$ m $时会迅速减少。此处显示的形状依赖性是非线性重力聚类的特征。非线性偏差（如果存在）将导致不同的形状依赖性。
The anisotrpy of the redshift space bispectrum $B^s(\mathbf{k_1},\mathbf{k_2},\mathbf{k_3})$, which contains a wealth of cosmological information, is completely quantified using multipole moments $\bar{B}^m_{\ell}(k_1,μ,t)$ where $k_1$, the length of the largest side, and $(μ,t)$ respectively quantify the size and shape of the triangle $(\mathbf{k_1},\mathbf{k_2},\mathbf{k_3})$. We present analytical expressions for all the multipoles which are predicted to be non-zero ($\ell \le 8, m \le 6$ ) at second order perturbation theory. The multipoles also depend on $β_1,b_1$ and $γ_2$, which quantify the linear redshift distortion parameter, linear bias and quadratic bias respectively. Considering triangles of all possible shapes, we analyse the shape dependence of all of the multipoles holding $k_1=0.2 \, {\rm Mpc}^{-1}, β_1=1, b_1=1$ and $γ_2=0$ fixed. The monopole $\bar{B}^0_0$, which is positive everywhere, is minimum for equilateral triangles. $\bar{B}_0^0$ increases towards linear triangles, and is maximum for linear triangles close to the squeezed limit. Both $\bar{B}^0_{2}$ and $\bar{B}^0_4$ are similar to $\bar{B}^0_0$, however the quadrupole $\bar{B}^0_2$ exceeds $\bar{B}^0_0$ over a significant range of shapes. The other multipoles, many of which become negative, have magnitudes smaller than $\bar{B}^0_0$. In most cases the maxima or minima, or both, occur very close to the squeezed limit. $\mid \bar{B}^m_{\ell} \mid $ is found to decrease rapidly if $\ell$ or $m$ are increased. The shape dependence shown here is characteristic of non-linear gravitational clustering. Non-linear bias, if present, will lead to a different shape dependence.
