We study an efficient way to enhance the measurability of the galaxy density and/or velocity power spectrum in redshift space. It is based on the angular decomposition with the Tripolar spherical harmonic (TripoSH) basis and applicable even to galaxy distributions in wide-angle galaxy surveys. While nontrivial multipole-mode mixings are inevitable in the covariance of the Legendre decomposition coefficient commonly used in the small-angle power spectrum analysis, our analytic computation of the covariance of the TripoSH decomposition coefficient shows that such mixings are absent by virtue of high separability of the TripoSH basis, yielding the minimum variance. Via the simple signal-to-noise ratio assessment, we confirm that the detectability improvement by the TripoSH decomposition approach becomes more significant at higher multipole modes, and, e.g., the hexadecapole of the density power spectrum has two orders of magnitude improvement. The TripoSH decomposition approach is expected to be applied to not only currently available survey data but also forthcoming wide-angle one, and to bring about something new or much more accurate cosmological information.
The dispersion measure (DM) of high-redshift $(z \gtrsim 6)$ transient objects such as Fast Radio Bursts can be a powerful tool to probe the intergalactic medium during the Epoch of Reionization. In this paper, we study the variance of the DMs of objects with the same redshift as a potential probe of the size distribution of ionized bubbles. We calculate the DM variance with a simple model with randomly-distributed spherical bubbles. It is found that the DM variance reflects the characteristics of the probability distribution of the bubble size. We find the variance can be measured precisely e…
This work introduces an unbiased minimum variance painting of the pixel domain CMB maps for both the missing and available sky regions. In the missing region, it generates CMB realizations that have identical statistical properties to the expected CMB signal; and in the available region, it significantly alleviate the unwanted residuals, e.g., the residual of EB-leakage. The time cost of this method follows $\sim$$ O(N_{side}^3)$ ($N_{side}$ is the map resolution parameter), which is similar to the fast spherical harmonic transforms and is much better than the traditional minimum variance meth…
As deeper observations discover increasingly distant galaxies, characterizing the properties of high-redshift galaxy populations will become increasingly challenging and paramount. We present a method for measuring the clustering bias of high-redshift galaxies from the field-to-field scatter in their number densities induced by cosmic variance. Multiple widely-separated fields are observed to provide a large number of statistically-independent samples of the high-redshift galaxy population. The expected Poisson uncertainty is removed from the measured dispersion in the distribution of galaxy n…
Deep pencil beam surveys (<1 deg^2) are of fundamental importance for studying the high-redshift universe. However, inferences about galaxy population properties are in practice limited by 'cosmic variance'. This is the uncertainty in observational estimates of the number density of galaxies arising from the underlying large-scale density fluctuations. This source of uncertainty can be significant, especially for surveys which cover only small areas and for massive high-redshift galaxies. Cosmic variance for a given galaxy population can be determined using predictions from cold dark matter th…
We examine the improvements in constraints on the linear growth factor G and its derivative f=d ln G / dln a that are available from the combination of a large-scale galaxy redshift survey with a weak gravitational lensing survey of background sources. In the linear perturbation theory limit, the bias-modulation method of McDonald & Seljak allows one to distinguish the real-space galaxy clustering from the peculiar velocity signal in each Fourier mode. The ratio of lensing signal to galaxy clustering in transverse modes yields the bias factor b of each galaxy subset (as per Pen 2004), hence ca…
We model the latest HST WFPC3/IR observations of > 100 galaxies at redshifts z=7-8 in terms of a hierarchical galaxy formation model with starburst activity. Our model provides a distribution of UV luminosities per dark matter halo of a given mass and a natural explanation for the fraction of halos hosting galaxies. The observed luminosity function is best fit with a minimum halo mass per galaxy of 10^{9.4+0.3-0.9} Msun, corresponding to a virial temperature of 10^{4.9+0.2-0.7} K. Extrapolating to faint, undetected galaxies, the total production rate of ionizing radiation depends critically on…
The estimation and analysis of large-scale bulk flow moments of peculiar velocity surveys is complicated by non-spherical survey geometry, the non-uniform sampling of the matter velocity field by the survey objects and the typically large measurement errors of the measured line-of-sight velocities. Previously, we have developed an optimal `minimum variance' (MV) weighting scheme for using peculiar velocity data to estimate bulk flow moments for idealized, dense and isotropic surveys with Gaussian radial distributions, that avoids many of these complications. These moments are designed to be ea…
Upcoming weak lensing surveys will survey large cosmological volumes to measure the growth of cosmological structure with time and thereby constrain dark energy. One major systematic uncertainty in this process is the calibration of the weak lensing shape distortions, or shears. Most upcoming surveys plan to test several aspects of their shear estimation algorithms using sophisticated image simulations that include realistic galaxy populations based on high-resolution data from the Hubble Space Telescope (HST). However, existing datasets from the (HST) cover very small cosmological volumes, so…
We use N-body/photometric galaxy simulations to examine the impact of sample variance of spectroscopic redshift samples on the accuracy of photometric redshift (photo-z) determination and calibration of photo-z errors. We estimate the biases in the cosmological parameter constraints from weak lensing and derive requirements on the spectroscopic follow-up for three different photo-z algorithms chosen to broadly span the range of algorithms available. We find that sample variance is much more relevant for the photo-z error calibration than for photo-z training, implying that follow-up requiremen…
Cosmological analyses of galaxy surveys rely on knowledge of the redshift distribution of their galaxy sample. This is usually derived from a spectroscopic and/or many-band photometric calibrator survey of a small patch of sky. The uncertainties in the redshift distribution of the calibrator sample include a contribution from shot noise, or Poisson sampling errors, but, given the small volume they probe, they are dominated by sample variance introduced by large-scale structures. Redshift uncertainties have been shown to constitute one of the leading contributions to systematic uncertainties in…
Strong gravitational lensing provides a powerful means for studying faint galaxies in the distant universe. By magnifying the apparent brightness of background sources, massive clusters enable the detection of galaxies fainter than the usual sensitivity limit for blank fields. However, this gain in effective sensitivity comes at the cost of a reduced survey volume and, in this {\it Letter}, we demonstrate there is an associated increase in the cosmic variance uncertainty. As an example, we show that the cosmic variance uncertainty of the high redshift population viewed through the Hubble Space…
Accurate mock catalogues are essential for assessing systematics in the cosmological analysis of large galaxy surveys. Anisotropic two-point clustering measurements from the same simulation show some scatter for different lines of sight (LOS), but are on average equal, due to cosmic variance. This results in scatter in the measured cosmological parameters. We use the OuterRim N-body simulation halo catalogue to investigate this, considering the 3 simulation axes as LOS. The quadrupole of the 2-point statistics is particularly sensitive to changes in the LOS, with sub-percent level differences …
In the present paper we study the radio sources in the NRAO VLA SKY Survey (NVSS) analysing its power spectrum and galaxy distribution. There is a discrepancy between the theoretical models in the literature and the data at large scales. A new model for NVSS is proposed combining the power spectrum data from NVSS and the galaxy distribution from the Combined EIS-NVSS Survey Of Radio Sources (CENSORS). Taken into account these two data sets the differences in the power spectrum at large scales are reduced, but there is still some tension between the two data sets. Different models are compared …
The low order moments, such as the bulk flow and shear, of the large scale peculiar velocity field are sensitive probes of the matter density fluctuations on very large scales. In practice, however, peculiar velocity surveys are usually sparse and noisy, which can lead to the aliasing of small scale power into what is meant to be a probe of the largest scales. Previously, we developed an optimal ``minimum variance'' (MV) weighting scheme, designed to overcome this problem by minimizing the difference between the measured bulk flow (BF) and that which would be measured by an ideal survey. Here …
Sample Variance Cancellation for Future Spectroscopic Surveys
Center for Theoretical Physics - a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院理论物理中心）；Department of Physics, University of California, Berkeley（加州大学伯克利分校物理系）；Berkeley Center for Cosmological Physics, UC Berkeley（加州大学伯克利分校宇宙学物理中心）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Using multiple tracers of large-scale structure allows to evade the limitations imposed by sampling variance for some parameters of interest in cosmology. We demonstrate the optimal way of carrying out a multitracer analysis in a galaxy redshift survey by considering the principal components of the shot noise matrix from two-point clustering statistics. We show how to construct two tracers that maximize the benefits of sampling variance and shot noise cancellation using optimal weights. On the basis of high-resolution N-body simulations of dark matter halos we apply this technique to the analy…
We simulate the effects of gravitational lensing on the source count of high redshift galaxies as projected to be observed by the Hubble Frontier Fields program and the James Webb Space Telescope (JWST) in the near future. Taking the mass density profile of the lensing object to be the singular isothermal sphere (SIS) or the Navarro-Frenk-White (NFW) profile, we model a lens residing at a redshift of z_L = 0.5 and explore the radial dependence of the resulting magnification bias and its variability with the velocity dispersion of the lens, the photometric sensitivity of the instrument, the red…
We present the improved visibility based Tapered Gridded Estimator (TGE) for the power spectrum of the diffuse sky signal. The visibilities are gridded to reduce the computation, and tapered through a convolution to suppress the contribution from the outer regions of the telescope's field of view. The TGE also internally estimates the noise bias, and subtracts this out to give an unbiased estimate of the power spectrum. An earlier version of the 2D TGE for the angular power spectrum $C_{\ell}$ is improved and then extended to obtain the 3D TGE for the power spectrum $P({\bf k})$ of the 21-cm b…
Forthcoming surveys will extend the understanding of cosmological large scale structures up to unprecedented redshift. According to this perspective, we present a fully relativistic framework to evaluate the impact of stochastic inhomogeneities on the determination of the Hubble constant. To this aim, we work within linear perturbation theory and relate the fluctuations of the luminosity distance-redshift relation, in the Cosmic Concordance model, to the intrinsic uncertainty associated to the measurement of $H_0$ from high-redshift surveys ($0.15\le z\le3.85$). We first present the detailed d…
Numerical simulations in cosmology require trade-offs between volume, resolution and run-time that limit the volume of the Universe that can be simulated, leading to sample variance in predictions of ensemble-average quantities such as the power spectrum or correlation function(s). Sample variance is particularly acute at large scales, which is also where analytic techniques can be highly reliable. This provides an opportunity to combine analytic and numerical techniques in a principled way to improve the dynamic range and reliability of predictions for clustering statistics. In this paper we …
We show how to obtain constraints on $β=f/b$, the ratio of the matter growth rate and the bias that quantifies the linear redshift-space distortions, that are independent of the cosmological model, using multiple tracers of large-scale structure. For a single tracer the uncertainties on $β$ are constrained by the uncertainties in the amplitude and shape of the power spectrum, which is limited by cosmic variance. However, for two or more tracers this limit does not apply, since taking the ratio of power spectra cosmic variance cancels out, and in the linear (Kaiser) approximation one measures d…
The Impact of Cosmic Variance and Satellites on JWST Clustering Measurements at Redshift around 6
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Center for Astrophysics | Harvard & Smithsonian（哈佛-史密森天体物理中心）；Leiden Observatory, Leiden University（莱顿大学莱顿天文台）
We explore the information theory entropy of a graph as a scalar to quantify the cosmic web. We find entropy values in the range between 1.5 and 3.2 bits. We argue that this entropy can be used as a discrete analogue of scalars used to quantify the connectivity in continuous density fields. After showing that the entropy clearly distinguishes between clustered and random points, we use simulations to gauge the influence of survey geometry, cosmic variance, redshift space distortions, redshift evolution, cosmological parameters and spatial number density. Cosmic variance shows the least importa…
Current and future generations of intensity mapping surveys promise dramatic improvements in our understanding of galaxy evolution and large-scale structure. An intensity map provides a census of the cumulative emission from all galaxies in a given region and redshift, including faint objects that are undetectable individually. Furthermore, cross-correlations between line intensity maps and galaxy redshift surveys are sensitive to the line intensity and clustering bias without the limitation of cosmic variance. Using the Fisher information matrix, we derive simple expressions describing sensit…
We consider the benefits of measuring cosmic statistical anisotropy from redshift-space correlators of the galaxy number density fluctuation and the peculiar velocity field without adopting the plane-parallel (PP) approximation. Since the correlators are decomposed using the general tripolar spherical harmonic (TripoSH) basis, we can deal with wide-angle contributions untreatable by the PP approximation, and at the same time, target anisotropic signatures can be cleanly extracted. We, for the first time, compute the covariance of the TripoSH decomposition coefficient and the Fisher matrix to f…
There is an approximately 9% discrepancy, corresponding to 2.4sigma, between two independent constraints on the expansion rate of the universe: one indirectly arising from the cosmic microwave background and baryon acoustic oscillations, and one more directly obtained from local measurements of the relation between redshifts and distances to sources. We argue that by taking into account the local gravitational potential at the position of the observer this tension - strengthened by the recent Planck results - is partially relieved and the concordance of the standard model of cosmology increase…
We present a data-driven method - heteroscedastic matrix factorization, a kind of probabilistic factor analysis - for modeling or performing dimensionality reduction on observed spectra or other high-dimensional data with known but non-uniform observational uncertainties. The method uses an iterative inverse-variance-weighted least-squares minimization procedure to generate a best set of basis functions. The method is similar to principal components analysis, but with the substantial advantage that it uses measurement uncertainties in a responsible way and accounts naturally for poorly measure…
