The power spectrum and bispectrum of dark matter tracers are key and complementary probes of the Universe. Next-generation surveys will deliver good measurements of the bispectrum, opening the door to improved cosmological constraints and the breaking of parameter degeneracies, from the combination of the power spectrum and bispectrum. Multi-tracer power spectra have been used to suppress cosmic variance and mitigate the effects of nuisance parameters and systematics. We present a bispectrum multi-tracer formalism that can be applied to next-generation survey data. Then we perform a simple Fisher analysis to illustrate qualitatively the improved precision on primordial non-Gaussianity that is expected to come from the bispectrum multi-tracer. In addition, we investigate the parametric dependence of conditional errors from multi-tracer power spectra and multi-tracer bispectra, on the differences between the biases and the number densities of two tracers. Our results suggest that optimal constraints arise from maximising the ratio of number densities, the difference between the linear biases, the difference between the quadratic biases, and the difference between the products $b_1\,b_Φ$ for each tracer, where $b_Φ$ is the bias for the primordial potential.
Calculating the primordial bispectrum predicted by a model of inflation and comparing it to what we see in the sky is very computationally intensive, necessitating layers of approximations and limiting the models which can be constrained. Exploiting the inherent separability of the tree level in-in formalism using expansions in separable basis functions provides a means by which to obviate some of these difficulties. Here, we develop this approach further into a practical and efficient numerical methodology which can be applied to a much wider and more complicated range of bispectrum phenomeno…
One major goal of upcoming large-scale-structure surveys is to constrain dark energy and modified gravity theories. In particular, galaxy clustering and gravitational lensing convergence are probes sensitive to modifications of general relativity. While the standard analysis for these surveys typically includes power spectra or 2-point correlation functions, it is known that the bispectrum contains more information, and could offer improved constraints on parameters when combined with the power spectra. However, the use of bispectra has been limited so far to one single probe, e.g. the lensing…
We develop a simple formalism of biased tracers that we dub $\mathit{Monkey\ bias}$. In this formalism, a biased tracer field is constructed directly in terms of the linear matter fluctuation field and the set of derivative operators acting on it. Such bias expansion is first organized based on the general structure of non-linear dynamical equations for the biased tracers. Further physical conditions, like the equivalence principle, are imposed on tree-level correlators utilising the consistency relations. We obtain the bias expansion up to the third-order in linear matter fluctuation in the g…
We present $\mathcal{O}(N^2)$ estimators for the small-scale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales, requiring orders of magnitude less computation time than Fast Fourier Transform based approaches alone. These methods are applicable to any tracer; simulation particles, halos or galaxies, and take advantage of the simple geometry of the box and periodicity to remove almost all dependence on large random particle catalogs. By working in configuration-space, b…
In this paper, we apply the multi-tracer technique to harmonic-space (i.e.\ angular) power spectra with a likelihood-based approach. This goes beyond the usual Fisher matrix formalism hitherto implemented in forecasts with angular statistics, opening up a window for future developments and direct application to available data sets. We also release a fully-operational modified version of the publicly available code CosmoSIS, where we consistently include all the add-ons presented in the previous papers of this series. The result is a modular cosmological parameter estimation suite for angular p…
Complex yet Hermitian: Gaussian covariance of cross-correlation and multi-tracer power spectra
Università degli Studi di Torino（都灵大学）；INFN – Istituto Nazionale di Fisica Nucleare, Sezione di Torino（意大利国家核物理研究所都灵分部）；INAF – Istituto Nazionale di Astrofisica, Osservatorio Astrofisico di Torino（意大利国家天体物理都灵天文台）；University of Western Cape（西开普大学）；INAF – Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Trieste（意大利国家天体物理的里雅斯特天文台）；INFN – Istituto Nazionale di Fisica Nucleare, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；IFPU – Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）
In astronomy and cosmology, significant effort is devoted to characterizing and understanding spatial cross-correlations between points - e.g. galaxy positions, high energy neutrino arrival directions, X-ray and AGN sources, and continuous field - e.g. weak lensing and Cosmic Microwave Background (CMB) maps. Recently, we introduced the $k$-nearest neighbor formalism to better characterize the clustering of discrete (point) datasets. Here we extend it to the point-field cross-correlation analysis. It combines $k$NN measurements of the point data set with measurements of the field smoothed on ma…
Line intensity mapping (LIM) is a rapidly emerging technique for constraining cosmology and galaxy formation using multi-frequency, low angular resolution maps. Many LIM applications crucially rely on cross-correlations of two line intensity maps, or of intensity maps with galaxy surveys or galaxy/CMB lensing. We present a consistent halo model to predict all these cross-correlations and enable joint analyses, in 3D redshift-space and for 2D projected maps. We extend the conditional luminosity function formalism to the multi-line case, to consistently account for correlated scatter between mul…
From photometric surveys to HI intensity mapping: Improving constraints on magnification biases while testing gravity
Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto（波尔图大学理学院物理与天文系）；Instituto de Astrofisica e Ciências do Espaço, Universidade do Porto CAUP（波尔图大学CAUP空间科学与天体物理研究所）；Department of Physics & Astronomy, University of the Western Cape（西开普大学物理与天文学系）
We develop a framework to compute the redshift space power spectrum (PS), with kernels beyond Einstein-de Sitter (EdS), that can be applied to a wide variety of generalized cosmologies. We build upon a formalism that was recently employed for standard cosmology in Chen, Vlah & White (2020), and utilize an expansion of the density-weighted velocity moment generating function that explicitly separates the magnitude of the $k$-modes and their angle to the line-of-sight direction dependencies. We compute the PS for matter and biased tracers to 1-loop Perturbation Theory (PT) and show that the expa…
Interloper bias in future large-scale structure surveys
下一代分光巡天将利用发射线星系作为示踪物，绘制可观测宇宙的大尺度结构。虽然每一次巡天都将用一条特定的发射线来绘制天空，但交错的发射线可以伪装成巡天在不同红移处的预期发射线。没有被移除的星系的干涉线会污染功率谱测量，混合各种红移的相关性并稀释真实信号。我们评估了功率谱污染的可能性，发现一个比0.2%更差的干扰者分数可能会使未来调查的功率谱测量偏差超过10%的统计误差，同时也会使功率谱推断产生偏差。我们还构建了一个预测宇宙学参数偏差的形式主义，证明了0.15%-0.3%的闯入者分数可能会使增长率偏差超过10%的误差，这可能会影响对即将到来的重力调查的约束。我们使用COSMOS模拟目录（CMC），与发射线重新缩放，以更好地再现最近的数据，预测潜在的闯入者分数的主焦点摄谱仪（PFS）和宽视场红外巡天望远镜（WFIRST）。我们发现，二次线识别，或确认星系红移找到相关的发射线，可以删除PFS的闯入者。对于WFIRST，我们使用CMC来预测WFIRST H $α$调查可以达到0.2%的目标，但需要灵敏的光学和近红外测光。对于WFIRST [OIII]调查，预测的闯入者比例达到百分之几，必须估计它们的影响并在统计上消除（例如，使用深度训练样本）。（节录）
