scholarly journals Wide-angle effects on galaxy ellipticity correlations

2021 ◽  
Author(s):  
Maresuke Shiraishi ◽  
Atsushi Taruya ◽  
Teppei Okumura ◽  
Kazuyuki Akitsu
Keyword(s):  
Cosmological Parameters ◽  
Three Dimensional ◽  
New Physics ◽  
Opening Angle ◽  
Wide Angle ◽  
Galaxy Surveys ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Cross Correlations ◽  
Three Dimensional Configuration

Abstract We show an efficient way to compute wide-angle or all-sky statistics of galaxy intrinsic alignment in three-dimensional configuration space. For this purpose, we expand the two-point correlation function using a newly introduced spin-dependent tripolar spherical harmonic basis. Therefore, the angular dependences on the two line-of-sight (LOS) directions pointing to each pair of objects, which are degenerate with each other in the conventional analysis under the small-angle or plane-parallel (PP) approximation, are unambiguously decomposed. By means of this, we, for the first time, compute the wide-angle auto and cross correlations between intrinsic ellipticities, number densities and velocities of galaxies, and compare them with the PP-limit results. For the ellipticity-ellipticity and density-ellipticity correlations, we find more than $10\%$ deviation from the PP-limit results if the opening angle between two LOS directions exceeds 30○ − 50○. It is also shown that even if the PP-limit result is strictly zero, the non-vanishing correlation is obtained over the various scales, arising purely from the curved-sky effects. Our results indicate the importance of the data analysis not relying on the PP approximation in order to determine the cosmological parameters more precisely and/or find new physics via ongoing and forthcoming wide-angle galaxy surveys.

scholarly journals Computing three-point correlation function randoms counts without the randoms catalogue

2019 ◽  
Vol 486 (1) ◽  
pp. L105-L109 ◽  
Author(s):  
David W Pearson ◽  
Lado Samushia
Keyword(s):  
Cosmological Parameters ◽  
Synthetic Data ◽  
Function Estimation ◽  
Point Function ◽  
Simple Method ◽  
Galaxy Surveys ◽  
Counting Algorithms ◽  
Data Points ◽  
Point Correlation ◽  
Point Correlation Function

ABSTRACT As we move towards future galaxy surveys, the three-point statistics will be increasingly leveraged to enhance the constraining power of the data on cosmological parameters. An essential part of the three-point function estimation is performing triplet counts of synthetic data points in random catalogues. Since triplet counting algorithms scale at best as $\mathcal {O}(N^2\log N)$ with the number of particles and the random catalogues are typically at least 50 times denser than the data; this tends to be by far the most time-consuming part of the measurements. Here, we present a simple method of computing the necessary triplet counts involving uniform random distributions through simple one-dimensional integrals. The method speeds up the computation of the three-point function by orders of magnitude, eliminating the need for random catalogues, with the simultaneous pair and triplet counting of the data points alone being sufficient.

scholarly journals Photometric Calibration and Large-Scale Clustering in the Universe

1994 ◽  
Vol 161 ◽  
pp. 295-300
Author(s):  
R. Fong ◽  
N. Metcalfe ◽  
T. Shanks
Keyword(s):  
Correlation Function ◽  
Large Scale ◽  
Three Dimensional ◽  
High Signal ◽  
Galaxy Surveys ◽  
Photometric Calibration ◽  
Peculiar Velocities ◽  
Redshift Surveys ◽  
Point Correlation ◽  
Point Correlation Function

The machine measurements of UK Schmidt plates have produced two very large galaxy surveys, the APM survey and the Edinburgh-Durham Southern Galaxy Catalogue (or COSMOS survey). These surveys can constrain the power on large scales of ≳ 10h −1 Mpc better than current redshift surveys, simply because such large numbers, ≳ 2 million galaxies to bJ ≤ 20.5, provide very high signal/noise in the estimated two-point correlation function for galaxies. Furthermore, the results for the three-dimensional galaxy two point correlation function, ξ(r), obtained from the measured projected function, ω(θ), should be quite robust for reasonable model number-redshift distributions, N(z), for these magnitude limits (see, e.g., Roche et al. 1993). Another clear advantage of measuring ω(θ) is that it is unaffected by the peculiar velocities of the galaxies, whereas they have an important effect on the corresponding ξ,(s) using galaxy redshift surveys.

scholarly journals Measuring Galaxy Bias from the High-Order Correlation Functions

1999 ◽  
Vol 183 ◽  
pp. 229-234
Author(s):  
Y.P. Jing
Keyword(s):  
Correlation Functions ◽  
Cosmological Parameters ◽  
High Order ◽  
Density Parameter ◽  
Theoretical Argument ◽  
Important Conclusion ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Redshift Survey ◽  
Galaxy Bias

In this talk, I will show how to determine the biasing factor b from the high-order moments of galaxies. The determination is based on the analytical modeling of primordial peaks and virialized halos and is independent of the currently unknown density parameter Ω0 and other cosmological parameters. The observed high-oder moments of the APM galaxies require that the biasing factor b be very close to 1, i.e. the optical galaxies are an unbiased tracer of the underlying mass distribution (on quasilinear scale). The theoretical argument can be easily generalized to the three-point correlation function and the bispectrum both of which can used as further observational tests to the important conclusion of b ≈ 1 drawn from the high-order moments. Finally I present our preliminary results of the three-point correlation functions for the Las Campanas Redshift Survey.

scholarly journals A Supersymmetric Hierarchical Model for Weakly Disordered 3d Semimetals

2020 ◽  
Vol 21 (11) ◽  
pp. 3499-3574
Author(s):  
Giovanni Antinucci ◽  
Luca Fresta ◽  
Marcello Porta
Keyword(s):  
Multiscale Analysis ◽  
Three Dimensional ◽  
Quantum Systems ◽  
Supersymmetric Model ◽  
Energy Bands ◽  
Algebraic Decay ◽  
Group Methods ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Renormalization Group Methods

Abstract In this paper, we study a hierarchical supersymmetric model for a class of gapless, three-dimensional, weakly disordered quantum systems, displaying pointlike Fermi surface and conical intersections of the energy bands in the absence of disorder. We use rigorous renormalization group methods and supersymmetry to compute the correlation functions of the system. We prove algebraic decay of the two-point correlation function, compatible with delocalization. A main technical ingredient is the multiscale analysis of massless bosonic Gaussian integrations with purely imaginary covariances, performed via iterative stationary phase expansions.

scholarly journals UNIT project: Universe N-body simulations for the Investigation of Theoretical models from galaxy surveys

2019 ◽  
Vol 487 (1) ◽  
pp. 48-59 ◽  
Author(s):  
Chia-Hsun Chuang ◽  
Gustavo Yepes ◽  
Francisco-Shu Kitaura ◽  
Marcos Pellejero-Ibanez ◽  
Sergio Rodríguez-Torres ◽  
...  
Keyword(s):  
Theoretical Models ◽  
Acoustic Oscillations ◽  
Cosmological Simulations ◽  
Galaxy Surveys ◽  
Suggested Technique ◽  
The Galaxy ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Cosmic Voids ◽  
Red Galaxies

Abstract We present the UNIT N-body cosmological simulations project, designed to provide precise predictions for non-linear statistics of the galaxy distribution. We focus on characterizing statistics relevant to emission line and luminous red galaxies in the current and upcoming generation of galaxy surveys. We use a suite of precise particle mesh simulations (fastpm) as well as with full N-body calculations with a mass resolution of ${\sim } 1.2\times 10^9\, h^{-1}$M⊙ to investigate the recently suggested technique of Angulo and Pontzen to suppress the variance of cosmological simulations. We study redshift-space distortions, cosmic voids, higher order statistics from z = 2 down to 0. We find that both two- and three-point statistics are unbiased. Over the scales of interest for baryon acoustic oscillations and redshift-space distortions, we find that the variance is greatly reduced in the two-point statistics and in the cross-correlation between haloes and cosmic voids, but is not reduced significantly for the three-point statistics. We demonstrate that the accuracy of the two-point correlation function for a galaxy survey with effective volume of 20 (h−1Gpc)3 is improved by about a factor of 40, indicating that two pairs of simulations with a volume of 1 (h−1Gpc)3 lead to the equivalent variance of ∼150 such simulations. The N-body simulations presented here thus provide an effective survey volume of about seven times the effective survey volume of Dark Energy Spectroscopic Instrument or Euclid. The data from this project, including dark matter fields, halo catalogues, and their clustering statistics, are publicly available.

scholarly journals CORRELATION FUNCTIONS OF A CONFORMAL FIELD THEORY IN THREE DIMENSIONS

1996 ◽  
Vol 11 (13) ◽  
pp. 1047-1059 ◽  
Author(s):  
S. GURUSWAMY ◽  
P. VITALE
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Correlation Functions ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Radius Of Curvature ◽  
Nonlinear Sigma Model ◽  
Long Distance ◽  
Point Correlation ◽  
Point Correlation Function

We derive explicit forms of the two-point correlation functions of the O(N) nonlinear sigma model at the critical point, in the large-N limit, on various three-dimensional manifolds of constant curvature. The two-point correlation function, G(x, y), is the only n-point correlation function which survives in this limit. We analyze the short distance and long distance behaviors of G(x, y). It is shown that G(x, y) decays exponentially with the Riemannian distance on the spaces R2×S1, S1×S1×R, S2×R, H2×R. The decay on R3 is of course a power law. We show that the scale for the correlation length is given by the geometry of the space and therefore the long distance behavior of the critical correlation function is not necessarily a power law even though the manifold is of infinite extent in all directions; this is the case of the hyperbolic space where the radius of curvature plays the role of a scale parameter. We also verify that the scalar field in this theory is a primary field with weight [Formula: see text]; we illustrate this using the example of the manifold S2×R whose metric is conformally equivalent to that of R3–{0} up to a reparametrization.

scholarly journals UV background fluctuations and three-point correlations in the large-scale clustering of the Lyman α forest

2019 ◽  
Vol 487 (4) ◽  
pp. 5346-5362 ◽  
Author(s):  
Suk Sien Tie ◽  
David H Weinberg ◽  
Paul Martini ◽  
Wei Zhu ◽  
Sébastien Peirani ◽  
...  
Keyword(s):  
Correlation Function ◽  
Large Scale ◽  
Signal To Noise Ratio ◽  
Mass Density ◽  
Three Dimensional ◽  
Mean Free Path ◽  
Density Fluctuations ◽  
Data Sets ◽  
Point Correlation ◽  
Point Correlation Function

ABSTRACT Using the Lyman α (Lyα) Mass Association Scheme, we make theoretical predictions for the three-dimensional three-point correlation function (3PCF) of the Lyα forest at redshift z = 2.3. We bootstrap results from the (100 h−1 Mpc)3 Horizon hydrodynamic simulation to a (1 h−1 Gpc)3N-body simulation, considering both a uniform ultraviolet background (UVB) and a fluctuating UVB sourced by quasars with a comoving nq ≈ 10−5h3 Mpc−3 placed either in massive haloes or randomly. On scales of 10–30 h−1 Mpc, the flux 3PCF displays hierarchical scaling with the square of the two-point correlation function (2PCF), but with an unusual value of Q ≡ ζ123/(ξ12ξ13 + ξ12ξ23 + ξ13ξ23) ≈ −4.5 that reflects the low bias of the Lyα forest and the anticorrelation between mass density and transmitted flux. For halo-based quasars and an ionizing photon mean free path of λ = 300 h−1 Mpc comoving, UVB fluctuations moderately depress the 2PCF and 3PCF, with cancelling effects on Q. For λ = 100 or 50 h−1 Mpc, UVB fluctuations substantially boost the 2PCF and 3PCF on large scales, shifting the hierarchical ratio to Q ≈ −3. We scale our simulation results to derive rough estimate of the detectability of the 3PCF in current and future observational data sets for the redshift range z = 2.1–2.6. At r = 10 and 20 h−1 Mpc, we predict a signal-to-noise ratio (SNR) of ∼9 and ∼7, respectively, for both Baryon Oscillation Spectroscopic Survey (BOSS) and extended BOSS (eBOSS), and ∼37 and ∼25 for Dark Energy Spectroscopic Instrument (DESI). At r = 40 h−1 Mpc the predicted SNR is lower by a factor of ∼3–5. Measuring the flux 3PCF would provide a novel test of the conventional paradigm of the Lyα forest and help separate the contributions of UVB fluctuations and density fluctuations to Lyα forest clustering, thereby solidifying its foundation as a tool of precision cosmology.

scholarly journals Trans-Planckian quantum corrections and inflationary vacuum fluctuations of non-minimally coupled scalar fields

2019 ◽  
Vol 34 (33) ◽  
pp. 1950275
Author(s):  
Hiroki Matsui
Keyword(s):  
Correlation Function ◽  
Effective Potential ◽  
Density Perturbation ◽  
Scalar Fields ◽  
New Physics ◽  
Quantum Corrections ◽  
Vacuum Fluctuations ◽  
Density Perturbations ◽  
Point Correlation ◽  
Point Correlation Function

In this paper, we discuss how trans-Planckian physics affects inflationary vacuum fluctuations and primordial density perturbations. The trans-Planckian problem during inflation has been widely discussed in the literature, but it is still under debate. We reconsider this problem by using the two-point correlation function of the non-minimally coupled scalar fields and constructing the effective potential with the adiabatic (WKB) regularization or approximation. First, we clearly show that the cut-off divergence of the quantum fluctuations does not drastically change during inflation under reasonable assumptions and the corrections can be embedded in standard effective potential. Thus, the UV effects on the primordial density perturbation are well translated into the effective potential. Then, we find out the modified effective potential from the inflationary fluctuations and show how the trans-Planckian or UV corrections change the potential during inflation. We clearly show that the new physics strongly affects the inflation potential during inflation and we obtain an inflationary constraint [Formula: see text], where [Formula: see text] is the interaction coupling at the UV scale [Formula: see text].

scholarly journals The self-similarity of weak lensing peaks

2019 ◽  
Vol 488 (4) ◽  
pp. 5833-5851 ◽  
Author(s):  
Christopher T Davies ◽  
Marius Cautun ◽  
Baojiu Li
Keyword(s):  
Signal To Noise Ratio ◽  
Cosmological Parameters ◽  
Weak Lensing ◽  
Self Similarity ◽  
Peak Separation ◽  
Wide Range ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Peak Abundance ◽  
Two Parameters

ABSTRACT We study the statistics of weak lensing convergence peaks, such as their abundance and two-point correlation function (2PCF), for a wide range of cosmological parameters Ωm and σ8 within the standard ΛCDM paradigm, focusing on intermediate-height peaks with signal-to-noise ratio (SNR) of 1.5–3.5. We find that the cosmology dependence of the peak abundance can be described by a one-parameter fitting formula that is accurate to within $\sim 3{{\ \rm per\ cent}}$. The peak 2PCFs are shown to feature a self-similar behaviour: if the peak separation is rescaled by the mean interpeak distance, catalogues with different minimum peak SNR values have identical clustering, which suggests that the peak abundance and clustering are closely interconnected. A simple fitting model for the rescaled 2PCF is given, which together with the peak abundance model above can predict peak 2PCFs with an accuracy better than $\sim 5{{\ \rm per\ cent}}$. The abundance and 2PCFs for intermediate peaks have very different dependencies on Ωm and σ8, implying that their combination can be used to break the degeneracy between these two parameters.

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