We perform a principal component analysis to assess ability of future observations to measure departures from General Relativity in predictions of the Poisson and anisotropy equations on linear scales. In particular, we focus on how the measurements of redshift-space distortions (RSD) observed from spectroscopic galaxy redshift surveys will improve the constraints when combined with lensing tomographic surveys. Assuming a Euclid-like galaxy imaging and redshift survey, we find that adding the 3D information decreases the statistical uncertainty by a factor between 3 and 10 compared to the case when only observables from lensing tomographic surveys are used. We also find that the number of well-constrained modes increases by a factor between 3 and 7. Our study indicates the importance of joint galaxy imaging and redshift surveys such as SuMIRe and Euclid to give more stringent tests of the ΛCDM model and to distinguish between various modified gravity and dark energy models.
An intervening galaxy acts as a gravitational lens and produces multiple images of a single source such as a remote galaxy. Galaxies have peculiar speeds in addition to the bulk motion arising due to the expansion of the universe. There is a difference in light arrival times between lensed images. We calculate more realistic time delays between lensed images when galaxy peculiar motions, that is the motion of the Lens, the Source and the Observer are taken into consideration neglecting the gravitomagnetic effects.
We show that peculiar velocities of Type Ia supernovae can be used to derive constraints on the sum of neutrino masses, $Σm_ν$, and dark energy equation of state, $w = w_0+w_a(1-a)$, from measurements of the magnitude-redshift relation, complementary to galaxy redshift and weak lensing surveys. Light from a supernova propagates through a perturbed Universe so the luminosity distance is modified from its homogeneous prediction. This modification is proportional to the matter density fluctuation and its time derivative due to gravitational lensing and peculiar velocity respectively. At low redsh…
In this work we address the issue of peculiar velocity measurement in a perturbed Friedmann universe using the deviations from measured luminosity distances of standard candles from background FRW universe. We want to show and quantify the statement that in intermediate redshifts ($0.5< z < 2$), deviations from the background FRW model are not uniquely governed by peculiar velocities. Luminosity distances are modified by gravitational lensing. We also want to indicate the importance of relativistic calculations for peculiar velocity measurement at all redshifts. For this task we discuss the re…
The cosmological peculiar velocity field (deviations from the pure Hubble flow) of matter carries significant information on dark energy, dark matter and the underlying theory of gravity on large scales. Peculiar motions of galaxies introduce systematic deviations between the observed galaxy redshifts z and the corresponding cosmological redshifts z_cos. A novel method for estimating the angular power spectrum of the peculiar velocity field based on observations of galaxy redshifts and apparent magnitudes m (or equivalently fluxes) is presented. This method exploits the fact that a mean relati…
GW number count can be used as a novel tracer of the large scale structure (LSS) in the luminosity distance space (LDS), just like galaxies in the redshift space. It is possible to obtain the $D_L-D_A$ duality relation with clustering effect. However, several LSS induced errors will contaminate the GW luminosity distance measurement, such as the peculiar velocity dispersion error of the host galaxy as well as the foreground lensing magnification. The distance uncertainties induced from these effects will degrade the GW clustering from a spectroscopic-like data down to a photometric-like data. …
Our peculiar motion in a homogeneous and isotropic universe imprints a dipole in the cosmic microwave background (CMB) temperature field and similarly imprints a dipole in the distribution of extragalactic radio sources on the sky. Each of these effects have been measured, however each of these measurements give different results for the velocity of our motion through the Universe: the radio dipole measurements finds the speed of our motion to be around three times larger than that of the CMB. Here we show the effects of the previously unconstrained lensing dipole, whereby necessarily local st…
We present a derivation of the cosmological distance-redshift relation up to second order in perturbation theory. In addition, we find the observed redshift and the lensing magnification to second order. We do not require that the density contrast is small, we only that the metric potentials and peculiar velocities are small. Thus our results apply into the nonlinear regime, and can be used for most dark energy models. We present the results in a form which can be readily computed in an N-body simulation. This paper accompanies arXiv:1207.2109, where the key results are summarised in a physica…
Cosmological tests of General Relativity: a principal component analysis
下一代弱透镜巡天将追踪从物质主导时代到今天的物质扰动和引力势的演变。随着对暗能量动力学的限制，他们将探索物质超密度、局部曲率和牛顿势之间的关系。我们用时间和尺度两个函数来解释LCDM模型中线性区域中这些关系的任何修改。我们执行主成分分析（PCA），以找到这些功能的本征模和本征值的调查，如DES和LSST。本文以Zhao et al.（2009）的PCA分析为基础，并在几个方面进行了显著扩展。特别是，我们认为在弱透镜调查中预期的一些系统性影响的影响。我们还提出了PCA的其他选择的两个功能需要参数化修改的线性尺度上的增长，并讨论他们的优点。我们分析了修正的增长函数和其他宇宙学参数之间的简并性，特别注意有效状态方程w（z）。最后，我们证明了PCA的效用作为一个有效的数据压缩阶段，使人们能够很容易地获得特定模型的参数约束，而无需从头开始重新计算Fisher矩阵。
We consider the dispersion on the supernova distance-redshift relation due to peculiar velocities and gravitational lensing, and the sensitivity of these effects to the amplitude of the matter power spectrum. We use the MeMo lensing likelihood developed by Quartin, Marra & Amendola (2014), which accounts for the characteristic non-Gaussian distribution caused by lensing magnification with measurements of the first four central moments of the distribution of magnitudes. We build on the MeMo likelihood by including the effects of peculiar velocities directly into the model for the moments. In or…
Radial redshift-space distortions due to peculiar velocities and other light-cone effects shape the maps we build of the Universe. We address the open question of their impact onto the monopole moment of the galaxy power spectrum, $P_0(k)$. Specifically, we use an upgraded numerical implementation of the LIGER method to generate $140$ mock galaxy density fields for a full Euclid-like survey and we measure $P_0(k)$ in each of them utilising a standard estimator. We compare the spectra obtained by turning on and off different effects. Our results show that wide-angle effects due to radial peculi…
Dark energy may be the first sign of new fundamental physics in the Universe, taking either a physical form or revealing a correction to Einsteinian gravity. Weak gravitational lensing and galaxy peculiar velocities provide complementary probes of General Relativity, and in combination allow us to test modified theories of gravity in a unique way. We perform such an analysis by combining measurements of cosmic shear tomography from the Canada-France Hawaii Telescope Lensing Survey (CFHTLenS) with the growth of structure from the WiggleZ Dark Energy Survey and the Six-degree-Field Galaxy Survey…
The skew-spectrum statistic introduced by Munshi & Heavens (2010) has recently been used in studies of non-Gaussianity from diverse cosmological data sets including the detection of primary and secondary non-Gaussianity of Cosmic Microwave Background (CMB) radiation. Extending previous work, focussed on independent estimation, here we deal with the question of joint estimation of multiple skew-spectra from the same or correlated data sets. We consider the optimum skew-spectra for various models of primordial non-Gaussianity as well as secondary bispectra that originate from the cross-correlati…
Dark matter halos represent the highest density peaks in the matter distribution. Conversely, cosmic voids are under-dense patches of the universe. Probing the mass distribution of the universe requires various approaches, including weak gravitational lensing that subtly modifies the shape of distant sources, and Doppler lensing that changes the apparent size and magnitude of objects due to peculiar velocities. In this work, we adopt both gravitational and Doppler lensing effects to study the underlying matter distribution in and around cosmic voids/halos. We use the relativistic $N$-body code…
We investigate three-point statistics in weak lensing convergence, through the integrated bispectrum. This statistic involves measuring power spectra in patches, and is thus easy to measure, and avoids the complexity of estimating the very large number of possible bispectrum configurations. The integrated bispectrum principally probes the squeezed limit of the bispectrum. To be useful as a set of summary statistics, accurate theoretical predictions of the signal are required, and, assuming Gaussian sampling distributions, the covariance matrix. In this paper, we investigate through simulations…
Forthcoming radio surveys will include full polarisation information, which can be potentially useful for weak lensing observations. We propose a new method to measure the (integrated) gravitational field between a source and the observer, by looking at the angle between the morphology of a radio galaxy and the orientation of the polarisation. For this we use the fact that, while the polarisation of a photon is parallel transported along the photon geodesic, the infinitesimal shape of the source, e.g. its principal axis in the case of an ellipse, is Lie transported. As an example, we calculate…
The unknown nature of dark energy motivates continued cosmological tests of large-scale gravitational physics. We present a new consistency check based on the relative amplitude of non-relativistic galaxy peculiar motions, measured via redshift-space distortion, and the relativistic deflection of light by those same galaxies traced by galaxy-galaxy lensing. We take advantage of the latest generation of deep, overlapping imaging and spectroscopic datasets, combining the Red Cluster Sequence Lensing Survey (RCSLenS), the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), the WiggleZ Dark …
When the gravitational lensing of the large-scale structure is calculated from a cosmological model a few assumptions enter: $(i)$ one assumes that the photons follow unperturbed background geodesics, which is usually referred to as the Born-approximation, $(ii)$ the lenses move slowly, $(iii)$ the source-redshift distribution is evaluated relative to the background quantities and $(iv)$ the lensing effect is linear in the gravitational potential. Even though these approximations are small individually they could sum up, especially since they include local effects such as the Sachs-Wolfe and p…
We test the usual hypothesis that the Cosmic Microwave Background (CMB) dipole, its largest anisotropy, is due to our peculiar velocity with respect to the Hubble flow by measuring independently the Doppler and aberration effects on the CMB using Planck 2018 data. We remove the spurious contributions from the conversion of intensity into temperature and arrive at measurements which are independent from the CMB dipole itself for both temperature and polarization maps and both SMICA and NILC component-separation methods. Combining these new measurements with the dipole one we get the first const…
The evolution of the virial overdensity $Δ_{\rm vir}$ for $Λ$CDM and seven dynamical dark-energy models is investigated in the extended spherical collapse model (SCM). Here the virialization process is naturally achieved by introducing shear and rotation instead of using the virial theorem. We generalise two approaches proposed in the literature and show that, regardless of the dark-energy model, the new virialization term can be calibrated on the peculiar velocity of the shell as measured from Einstein-de Sitter simulations. The two virialization recipes qualitatively reproduce the features o…
Multimodality in galaxy clusters from SDSS DR8: substructure and velocity distribution
我们搜索的存在下的子结构，一个非高斯，不对称的速度分布的星系，和大的特殊速度的星系团中的主要星系至少有50个成员星系，从SDSS DR 8绘制。我们采用了一些3D，2D和1D的测试来分析星系团的分布：3D正常混合建模，Dressler-Shectman测试，Anderson-Darling和Shapiro-Wilk测试和其他。我们找到了主要星系的特殊速度，并使用主成分分析来表征我们的结果。根据3D正态混合模型，我们样本中超过80%的簇具有子结构，Dressler-Shectman（DS）检验显示约70%的簇具有子结构。星系团中主要星系特有速度的中值为206 km/s（均方根速度的41%）。超过20%的星系团中的星系速度表现出明显的非高斯性。虽然多维正态混合模型是更敏感的比DS测试在解决子结构的星系团的天空分布，DS测试确定更好的子结构表示为尾巴的速度分布的星系。更丰富，更大，更明亮的星系团具有更大的子结构和更大的（与均方根速度相比）主星系的特有速度。对星系团的子结构指标和物理参数的主成分分析表明，星系团是一个复杂的天体，其性质不能用少量的参数来解释，也不能用单一的检验来界定。子结构的存在，非高斯的速度分布，以及大的奇特的速度的主要星系，表明我们的样本中的大部分星系团是动态年轻的。
Weak lensing (WL) promises to be a particularly sensitive probe of both the growth of large scale structure (LSS) as well as the fundamental relation between matter density perturbations and metric perturbations, thus providing a powerful tool with which we may constrain modified theories of gravity (MG) on cosmological scales. Future deep, wide-field WL surveys will provide an unprecedented opportunity to constrain deviations from General Relativity (GR). Employing a three-dimensional (3D) analysis based on the spherical Fourier-Bessel (sFB) expansion, we investigate the extent to which MG th…
We address key points for an efficient implementation of likelihood codes for modern weak lensing large-scale structure surveys. Specifically, we focus on the joint weak lensing convergence power spectrum-bispectrum probe and we tackle the numerical challenges required by a realistic analysis. Under the assumption of (multivariate) Gaussian likelihoods, we have developed a high performance code that allows highly parallelised prediction of the binned tomographic observables and of their joint non-Gaussian covariance matrix accounting for terms up to the 6-point correlation function and super-s…
The supernova (SN) Hubble diagram residual contains valuable information on both the present matter power spectrum and its growth history. In this paper we show that this information can be retrieved with precision by combining both peculiar velocity and weak-lensing analysis on the data. To wit, peculiar velocity induces correlations on the nearby SN while lensing induces a non-Gaussian dispersion in faraway objects. We show that both effects have almost orthogonal degeneracies and discuss how they can be extracted simultaneously from the data. We analyze the JLA supernova catalog in a 14-dim…
The Sunyaev--Zel'dovich (SZ) effect is a global distortion of the Cosmic Microwave Background (CMB) spectrum as a result of its interaction with a hot electron plasma in the intracluster medium of large structures gravitationally viralized such as galaxy clusters (GC). Furthermore, this~hot gas of electrons emits X-rays due to its fall in the gravitational potential well of the GC. The~analysis of SZ and X-ray data provides a method for calculating distances to GC at high redshifts. On the other hand, many galaxies and GC produce a Strong Gravitational Lens (SGL) effect, which has become a use…
Weak gravitational lensing shear could be measured far more precisely if information about unlensed attributes of source galaxies were available. Disk galaxy velocity fields supply such information, at least in principle, with idealized models predicting orders of magnitude more Fisher information when velocity field observations are used to complement images. To test the level at which realistic features of disk galaxies (warps, bars, spiral arms, and other substructure) inject noise or bias into such shear measurements, we fit an idealized disk model, including shear, to unsheared galaxies i…
The simple assumption of an instantaneous reionization of the Universe may bias estimates of cosmological parameters. In this paper a model-independent principal component method for the reionization history is applied to give constraints on the cosmological parameters from recent Planck 2015 data. We find that the Universe are not completely reionized at redshifts $z \ge 8.5$ at 95% CL. Both the reionization optical depth and the matter fluctuation amplitude are higher than but consistent with those obtained in the standard instantaneous reionization scheme. The high estimated value of the ma…
Weak gravitational lensing is a powerful cosmological probe, with non--Gaussian features potentially containing the majority of the information. We examine constraints on the parameter triplet $(Ω_m,w,σ_8)$ from non-Gaussian features of the weak lensing convergence field, including a set of moments (up to $4^{\rm th}$ order) and Minkowski functionals, using publicly available data from the 154deg$^2$ CFHTLenS survey. We utilize a suite of ray--tracing N-body simulations spanning 91 points in $(Ω_m,w,σ_8)$ parameter space, replicating the galaxy sky positions, redshifts and shape noise in the C…
Objects falling into an overdensity appear larger on its near side and smaller on its far side than other objects at the same redshift. This produces a dipolar pattern of magnification, primarily as a consequence of the Doppler effect. At low redshift this Doppler magnification completely dominates the usual integrated gravitational lensing contribution to the lensing magnification. We show that one can optimally observe this pattern by extracting the dipole in the cross-correlation of number counts and galaxy sizes. This dipole allows us to almost completely remove the contribution from gravi…
The galaxy cluster RX J0603.3+4214 at z=0.225 is one of the rarest clusters boasting an extremely large (~2 Mpc) radio-relic. Because of the remarkable morphology of the relic, the cluster is nicknamed "Toothbrush Cluster". Although the cluster's underlying mass distribution is one of the critical pieces of information needed to reconstruct the merger scenario responsible for the puzzling radio-relic morphology, its proximity to the Galactic plane b~10 deg has imposed significant observational challenges. We present a high-resolution weak-lensing study of the cluster with Subaru/Suprime Cam an…
We explore how the galaxy stellar spins acquire a peculiar tendency of being aligned with the major principal axes of the local tidal fields, in contrast to their DM counterparts which tend to be perpendicular to them, regardless of their masses. Analyzing the halo and subhalo catalogs from the IllustrisTNG 300 hydrodynamic simulations at $z\le 1$, we determine the cosines of the alignment angles, $\cosα$, between the galaxy stellar and DM spins. Creating four $\cosα$-selected samples of the galaxies and then controlling them to share the same density and mass distributions, we determine the a…
We study how the shape of the spectrum of primordial gravitational waves can be constrained by future experiments looking at the B-mode of the Cosmic Microwave Background (CMB) polarization. We implement a Principal Component Analysis (PCA) including the effects of diffuse foreground residuals, following component separation, in the uncertainty of CMB angular power spectra, and taking into account the gravitational lensing by Large Scale Structure. We perform our study by considering the capabilities of future B-mode CMB experiments such as LiteBIRD, the Simons Observatory (SO) and Stage-IV (C…
We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in one-dimensional marginal distributions of shear two-point correlation functions in simulated weak lensing data. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the non-Gaussianity scales with survey area. We show that there is no significant bias in one-dimensional posteriors of $Ω_{\rm m}$ and $σ_{\rm 8}$ due to the non-Gaussian likelihood distributions of shear …
Towards the Two-Loop EFTofLSS in Galaxy Lensing Surveys
Stony Brook University（石溪大学）；C.N. Yang Institute for Theoretical Physics, Stony Brook University（石溪大学陈省身理论物理研究所）；Ludwig-Maximilians-Universität（路德维希-马克西米利安大学）；Kavli Institute for Cosmology Cambridge（卡弗里宇宙学剑桥研究所）；University of Cambridge（剑桥大学）；University of Arizona（亚利桑那大学）
The aberration and Doppler coupling effects of the Cosmic Microwave Background (CMB) were recently measured by the Planck satellite. The most straightforward interpretation leads to a direct detection of our peculiar velocity $β$, consistent with the measurement of the well-known dipole. In this paper we discuss the assumptions behind such interpretation. We show that Doppler-like couplings appear from two effects: our peculiar velocity and a second order large-scale effect due to the dipolar part of the gravitational potential. We find that the two effects are exactly degenerate but only if w…
We present measurements of both scale- and time-dependent deviations from the standard gravitational field equations. These late-time modifications are introduced separately for relativistic and non-relativistic particles, by way of the parameters $G_{\rm matter}(k,z)$ and $G_{\rm light}(k,z)$ using two bins in both scale and time, with transition wavenumber $0.01$ Mpc$^{-1}$ and redshift 1. We emphasize the use of two dynamical probes to constrain this set of parameters, galaxy power spectrum multipoles and the direct peculiar velocity power spectrum, which probe fluctuations on different sca…
3D data compression techniques can be used to determine the natural basis of radial eigenmodes that encode the maximum amount of information in a tomographic large-scale structure survey. We explore the potential of the Karhunen-Loève decomposition in reducing the dimensionality of the data vector for cosmic shear measurements, and apply it to the final data from the \cfh survey. We find that practically all of the cosmological information can be encoded in one single radial eigenmode, from which we are able to reproduce compatible constraints with those found in the fiducial tomographic analy…
