scholarly journals Cosmological parameters from the likelihood analysis of the galaxy power spectrum and bispectrum in real space

2021 ◽  
Vol 2021 (11) ◽  
pp. 038
Author(s):  
Andrea Oddo ◽  
Federico Rizzo ◽  
Emiliano Sefusatti ◽  
Cristiano Porciani ◽  
Pierluigi Monaco
Keyword(s):  
Power Spectrum ◽  
Cosmological Parameters ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
Real Space ◽  
Tree Level ◽  
Large Set ◽  
Cross Covariance ◽  
Likelihood Analysis ◽  
The Galaxy

Abstract We present a joint likelihood analysis of the halo power spectrum and bispectrum in real space. We take advantage of a large set of numerical simulations and of an even larger set of halo mock catalogs to provide a robust estimate of the covariance properties. We derive constraints on bias and cosmological parameters assuming a theoretical model from perturbation theory at one-loop for the power spectrum and tree-level for the bispectrum. By means of the Deviance Information Criterion, we select a reference bias model dependent on seven parameters that can describe the data up to k max,P = 0.3 h Mpc-1 for the power spectrum and k max,B = 0.09 h Mpc-1 for the bispectrum at redshift z = 1. This model is able to accurately recover three selected cosmological parameters even for the rather extreme total simulation volume of 1000h -3 Gpc3. With the same tools, we study how relations among bias parameters can improve the fit while reducing the parameter space. In addition, we compare common approximations to the covariance matrix against the full covariance estimated from the mocks, and quantify the (non-negligible) effect of ignoring the cross-covariance between the two statistics. Finally, we explore different selection criteria for the triangular configurations to include in the analysis, showing that excluding nearly equilateral triangles rather than simply imposing a fixed maximum k max,B on all triangle sides can lead to a better exploitation of the information contained in the bispectrum.

Imaging the Cosmic Microwave Background with the Arcminute Cosmology Bolometer Array Receiver

2005 ◽  
Vol 216 ◽  
pp. 43-50
Author(s):  
J. B. Peterson ◽  
A. K. Romer ◽  
P. L. Gomez ◽  
P. A. R. Ade ◽  
J. J. Bock ◽  
...  
Keyword(s):  
Power Spectrum ◽  
Cosmic Microwave Background ◽  
Cosmological Parameters ◽  
Galaxy Cluster ◽  
Clusters Of Galaxies ◽  
Microwave Background ◽  
Bolometer Array ◽  
The Galaxy ◽  
Millimeter Wave Receiver ◽  
Array Receiver

The Arcminute Cosmology Bolometer Array Receiver (Acbar) is a multifrequency millimeter-wave receiver optimized for observations of the Cosmic Microwave Background (CMB) and the Sunyaev-Zel'dovich (SZ) effect in clusters of galaxies. Acbar was installed on the 2.1 m Viper telescope at the South Pole in January 2001 and the results presented here incorporate data through July 2002. The power spectrum of the CMB at 150 GHz over the range ℓ = 150 — 3000 measured by Acbar is presented along with estimates for the values of the cosmological parameters within the context of ΛCDM models. The inclusion of ΩΛ greatly improves the fit to the power spectrum. Three-frequency images of the SZ decrement/increment are also presented for the galaxy cluster 1E0657–67.

scholarly journals Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space

2020 ◽  
Vol 497 (2) ◽  
pp. 1684-1711 ◽  
Author(s):  
Naonori S Sugiyama ◽  
Shun Saito ◽  
Florian Beutler ◽  
Hee-Jong Seo
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Shot Noise ◽  
Signal To Noise Ratio ◽  
Covariance Matrices ◽  
Theory Approach ◽  
Cross Covariance ◽  
The Galaxy ◽  
The Cross ◽  
Non Gaussian

ABSTRACT In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects, and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the autocovariance of the bispectrum in redshift space. We test the validity of our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order PT works because the shot-noise corrections for the Patchy mocks are more dominant than other higher order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise ratio of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.

scholarly journals Primordial non-Gaussianity from biased tracers: likelihood analysis of real-space power spectrum and bispectrum

2021 ◽  
Vol 2021 (05) ◽  
pp. 015
Author(s):  
Azadeh Moradinezhad Dizgah ◽  
Matteo Biagetti ◽  
Emiliano Sefusatti ◽  
Vincent Desjacques ◽  
Jorge Noreña
Keyword(s):  
Power Spectrum ◽  
Real Space ◽  
Likelihood Analysis

scholarly journals Mixed dark matter: matter power spectrum and halo mass function

2021 ◽  
Vol 2021 (12) ◽  
pp. 044
Author(s):  
G. Parimbelli ◽  
G. Scelfo ◽  
S.K. Giri ◽  
A. Schneider ◽  
M. Archidiacono ◽  
...  
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Large Scale ◽  
Cosmological Parameters ◽  
Mass Function ◽  
Large Set ◽  
Cluster Number ◽  
Matter Power Spectrum ◽  
Wide Range ◽  
The Impact

Abstract We investigate and quantify the impact of mixed (cold and warm) dark matter models on large-scale structure observables. In this scenario, dark matter comes in two phases, a cold one (CDM) and a warm one (WDM): the presence of the latter causes a suppression in the matter power spectrum which is allowed by current constraints and may be detected in present-day and upcoming surveys. We run a large set of N-body simulations in order to build an efficient and accurate emulator to predict the aforementioned suppression with percent precision over a wide range of values for the WDM mass, Mwdm, and its fraction with respect to the totality of dark matter, fwdm. The suppression in the matter power spectrum is found to be independent of changes in the cosmological parameters at the 2% level for k≲ 10 h/Mpc and z≤ 3.5. In the same ranges, by applying a baryonification procedure on both ΛCDM and CWDM simulations to account for the effect of feedback, we find a similar level of agreement between the two scenarios. We examine the impact that such suppression has on weak lensing and angular galaxy clustering power spectra. Finally, we discuss the impact of mixed dark matter on the shape of the halo mass function and which analytical prescription yields the best agreement with simulations. We provide the reader with an application to galaxy cluster number counts.

scholarly journals Generating approximate halo catalogues for blind challenges in precision cosmology

2019 ◽  
Vol 485 (2) ◽  
pp. 2407-2416 ◽  
Author(s):  
Lehman H Garrison ◽  
Daniel J Eisenstein
Keyword(s):  
Dark Matter ◽  
Transfer Function ◽  
Power Spectrum ◽  
High Precision ◽  
Real Space ◽  
Dark Matter Halo ◽  
The Real ◽  
The Galaxy ◽  
Similar Accuracy ◽  
Better Than

ABSTRACT We present a method for generating suites of dark matter halo catalogues with only a few N-body simulations, focusing on making small changes to the underlying cosmology of a simulation with high precision. In the context of blind challenges, this allows us to re-use a simulation by giving it a new cosmology after the original cosmology is revealed. Starting with full N-body realizations of an original cosmology and a target cosmology, we fit a transfer function that displaces haloes in the original so that the galaxy/HOD power spectrum matches that of the target cosmology. This measured transfer function can then be applied to a new realization of the original cosmology to create a new realization of the target cosmology. For a 1 per cent change in σ8, we achieve 0.1 per cent accuracy to $k = 1\, h\, \mathrm{Mpc}^{-1}$ in the real-space power spectrum; this degrades to 0.3 per cent when the transfer function is applied to a new realization. We achieve similar accuracy in the redshift-space monopole and quadrupole. In all cases, the result is better than the sample variance of our $1.1\, h^{-1}\, \mathrm{Gpc}$ simulation boxes.

scholarly journals Computing the small-scale galaxy power spectrum and bispectrum in configuration space

2019 ◽  
Vol 492 (1) ◽  
pp. 1214-1242 ◽  
Author(s):  
Oliver H E Philcox ◽  
Daniel J Eisenstein
Keyword(s):  
Power Spectrum ◽  
Configuration Space ◽  
Fourier Transforms ◽  
Cosmological Parameters ◽  
Power Spectra ◽  
Small Scale ◽  
High K ◽  
Cross Covariance ◽  
Small Scales ◽  
Point Correlation

ABSTRACT We present a new class of estimators for computing small-scale power spectra and bispectra in configuration space via weighted pair and triple counts, with no explicit use of Fourier transforms. Particle counts are truncated at $R_0\sim 100\, h^{-1}\, \mathrm{Mpc}$ via a continuous window function, which has negligible effect on the measured power spectrum multipoles at small scales. This gives a power spectrum algorithm with complexity $\mathcal {O}(NnR_0^3)$ (or $\mathcal {O}(Nn^2R_0^6)$ for the bispectrum), measuring N galaxies with number density n. Our estimators are corrected for the survey geometry and have neither self-count contributions nor discretization artefacts, making them ideal for high-k analysis. Unlike conventional Fourier-transform-based approaches, our algorithm becomes more efficient on small scales (since a smaller R0 may be used), thus we may efficiently estimate spectra across k-space by coupling this method with standard techniques. We demonstrate the utility of the publicly available power spectrum algorithm by applying it to BOSS DR12 simulations to compute the high-k power spectrum and its covariance. In addition, we derive a theoretical rescaled-Gaussian covariance matrix, which incorporates the survey geometry and is found to be in good agreement with that from mocks. Computing configuration- and Fourier-space statistics in the same manner allows us to consider joint analyses, which can place stronger bounds on cosmological parameters; to this end we also discuss the cross-covariance between the two-point correlation function and the small-scale power spectrum.

scholarly journals Compact groups from semi-analytical models of galaxy formation – II. Different assembly channels

2021 ◽  
Vol 503 (1) ◽  
pp. 394-405
Author(s):  
E Díaz-Giménez ◽  
A Zandivarez ◽  
G A Mamon
Keyword(s):  
Galaxy Formation ◽  
Cosmological Parameters ◽  
Real Space ◽  
Analytical Models ◽  
Compact Groups ◽  
Density Parameter ◽  
Centre Of Mass ◽  
Trace Back ◽  
The Galaxy

ABSTRACT We study the formation of over 6000 compact groups (CGs) of galaxies identified in mock redshift-space galaxy catalogues built from semi-analytical models of galaxy formation (SAMs) run on the Millennium Simulations. We select CGs of four members in our mock SDSS galaxy catalogues and, for each CG, we trace back in time the real-space positions of the most massive progenitors of their four galaxies. By analysing the evolution of the distance of the galaxy members to the centre of mass of the group, we identify four channels of CG formation. The classification of these assembly channels is performed with an automatic recipe inferred from a preliminary visual inspection and based on the orbit of the galaxy with the fewest number of orbits. Most CGs show late assembly, with the last galaxy arriving on its first or second passage, while only 10–20 per cent form by the gradual contraction of their orbits by dynamical friction, and only a few per cent forming early with little subsequent contraction. However, a SAM from a higher resolution simulation leads to earlier assembly. Assembly histories of CGs also depend on cosmological parameters. At similar resolution, CGs assemble later in SAMs built on parent cosmological simulations of high density parameter. Several observed properties of mock CGs correlate with their assembly history: early-assembling CGs are smaller, with shorter crossing times, and greater magnitude gaps between their brightest two members, and their brightest galaxies have smaller spatial offsets and are more passive.

scholarly journals Contributions from primordial non-Gaussianity and general relativity to the galaxy power spectrum

2021 ◽  
Vol 2021 (12) ◽  
pp. 025
Author(s):  
Rebeca Martinez-Carrillo ◽  
Juan Carlos Hidalgo ◽  
Karim A. Malik ◽  
Alkistis Pourtsidou
Keyword(s):  
General Relativity ◽  
Power Spectrum ◽  
Stage Iv ◽  
Real Space ◽  
Order Effects ◽  
Leading Order ◽  
Bias Parameter ◽  
Matter Power Spectrum ◽  
The Galaxy ◽  
The One

Abstract We compute the real space galaxy power spectrum, including the leading order effects of General Relativity and primordial non-Gaussianity from the f NL and g NL parameters. Such contributions come from the one-loop matter power spectrum terms dominant at large scales, and from the factors of the non-linear bias parameter b NL (akin to the Newtonian b ϕ). We assess the detectability of these contributions in Stage-IV surveys. In particular, we note that specific values of the bias parameter may erase the primordial and relativistic contributions to the configuration space power spectrum.

scholarly journals Covariance of the galaxy angular power spectrum with the halo model

2018 ◽  
Vol 615 ◽  
pp. A1 ◽  
Author(s):  
Fabien Lacasa
Keyword(s):  
Perturbation Theory ◽  
Shot Noise ◽  
Real Space ◽  
Density Fluctuations ◽  
Tree Level ◽  
Analytical Prediction ◽  
Angular Power Spectrum ◽  
Sample Covariance ◽  
The Galaxy ◽  
Non Gaussian

As the determination of density fluctuations becomes more precise with larger surveys, it becomes more important to account for the increased covariance due to the non-linearity of the field. Here I have focussed on the galaxy density, with analytical prediction of the non-Gaussianity using the halo model coupled with standard perturbation theory in real space. I carried out an exact and exhaustive derivation of all tree-level terms of the non-Gaussian covariance of the galaxyCℓ, with the computation developed up to the third order in perturbation theory and local halo bias, including the non-local tidal tensor effect. A diagrammatic method was used to derive the involved galaxy 3D trispectra, including shot-noise contributions. The projection to the angular covariance was derived in all trispectra cases with and without Limber’s approximation, with the formulae being of potential interest for other observables than galaxies. The effect of subtracting shot-noise from the measured spectrum is also discussed, and does simplify the covariance, though some non-Gaussian shot-noise terms still remain. I make the link between this complete derivation and partial terms which have been used previously in the literature, including super-sample covariance (SSC). I uncover a wealth of additional terms which were not previously considered, including a whole new class which I dub braiding terms as it contains multipole-mixing kernels. The importance of all these new terms is discussed with analytical arguments. I find that they become comparable to, if not bigger than, SSC if the survey is large or deep enough to probe scales comparable with the matter-radiation equalitykeq. A short self-contained summary of the equations is provided in Sect. 9 for the busy reader, ready to be implemented numerically for analysis of current and future galaxy surveys.

scholarly journals The redshift-space momentum power spectrum – I. Optimal estimation from peculiar velocity surveys

2019 ◽  
Vol 487 (4) ◽  
pp. 5209-5234 ◽  
Author(s):  
Cullan Howlett
Keyword(s):  
Power Spectrum ◽  
Measurement Errors ◽  
Cosmological Parameters ◽  
Power Spectra ◽  
Optimal Estimation ◽  
Peculiar Velocity ◽  
Optimal Weights ◽  
Peculiar Velocities ◽  
Redshift Surveys ◽  
The Galaxy

Abstract Low redshift surveys of galaxy peculiar velocities provide a wealth of cosmological information. We revisit the idea of extracting this information by directly measuring the redshift-space momentum power spectrum from such surveys. We provide a comprehensive theoretical and practical framework for estimating and fitting this from data, analogous to well-understood techniques used to measure the galaxy density power spectrum from redshift surveys. We formally derive a new estimator, which includes the effects of shot noise and survey geometry; we evaluate the variance of the estimator in the Gaussian regime; we compute the optimal weights for the estimator; we demonstrate that the measurements are Gaussian distributed, allowing for easy extraction of cosmological parameters; and we explore the effects of peculiar velocity (PV) measurement errors. We finish with a proof-of-concept using realistic mock galaxy catalogues, which demonstrates that we can measure and fit both the redshift-space galaxy density and momentum power spectra from PV surveys and that including the latter substantially improves our constraints on the growth rate of structure. We also provide theoretical descriptions for modelling the non-linear redshift-space density and momentum power spectrum multipoles, and forecasting the constraints on cosmological parameters using the Fisher information contained in these measurements for arbitrary weights. These may be useful for measurements of the galaxy density power spectrum even in the absence of peculiar velocities.

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