scholarly journals One-Point Statistics Matter in Extended Cosmologies

2021 ◽  
Author(s):  
Alex Gough ◽  
Cora Uhlemann
Keyword(s):  
Power Spectrum ◽  
Large Deviation ◽  
Matter Field ◽  
Gaussian Fields ◽  
Fundamental Physics ◽  
Matter Power Spectrum ◽  
Gaussian Statistic ◽  
Linear Information ◽  
Point Correlation ◽  
Non Gaussian

The late universe contains a wealth of information about fundamental physics and gravity, wrapped up in non-Gaussian fields. To make use of as much information as possible it is necessary to go beyond two-point statistics. Rather than going to higher order N-point correlation functions, we demonstrate that the probability distribution function (PDF) of spheres in the matter field (a one-point function) already contains a significant amount of this non-Gaussian information. The matter PDF dissects different density environments which are lumped together in two-point statistics, making it particularly useful for probing modifications of gravity or expansion history. Our approach in Cataneo et. al. 2021 extends the success of Large Deviation Theory for predicting the matter PDF in ΛCDM in these “extended” cosmologies. A Fisher forecast demonstrates the information content in the matter PDF via constraints for a Euclid-like survey volume combining the 3D matter PDF with the 3D matter power spectrum. Adding the matter PDF halves the uncertainties on parameters in an evolving dark energy model, relative to the power spectrum alone. Additionally, the matter PDF contains enough non-linear information to substantially increase the detection significance of departures from General Relativity, with improvements up to six times the power spectrum alone. This analysis demonstrates that the matter PDF is a promising non-Gaussian statistic for extracting cosmological information, particularly for beyond ΛCDM models.

scholarly journals Cosmological model parameter dependence of the matter power spectrum covariance from the DEUS-PUR Cosmo simulations

2020 ◽  
Vol 500 (2) ◽  
pp. 2532-2542
Author(s):  
Linda Blot ◽  
Pier-Stefano Corasaniti ◽  
Yann Rasera ◽  
Shankar Agarwal
Keyword(s):  
Dark Energy ◽  
Power Spectrum ◽  
Cold Dark Matter ◽  
Matter Density ◽  
Density Fluctuations ◽  
Matrix Analysis ◽  
Model Parameter ◽  
Matter Power Spectrum ◽  
Non Gaussian ◽  
The Impact

ABSTRACT Future galaxy surveys will provide accurate measurements of the matter power spectrum across an unprecedented range of scales and redshifts. The analysis of these data will require one to accurately model the imprint of non-linearities of the matter density field. In particular, these induce a non-Gaussian contribution to the data covariance that needs to be properly taken into account to realize unbiased cosmological parameter inference analyses. Here, we study the cosmological dependence of the matter power spectrum covariance using a dedicated suite of N-body simulations, the Dark Energy Universe Simulation–Parallel Universe Runs (DEUS-PUR) Cosmo. These consist of 512 realizations for 10 different cosmologies where we vary the matter density Ωm, the amplitude of density fluctuations σ8, the reduced Hubble parameter h, and a constant dark energy equation of state w by approximately $10{{\ \rm per\ cent}}$. We use these data to evaluate the first and second derivatives of the power spectrum covariance with respect to a fiducial Λ-cold dark matter cosmology. We find that the variations can be as large as $150{{\ \rm per\ cent}}$ depending on the scale, redshift, and model parameter considered. By performing a Fisher matrix analysis we explore the impact of different choices in modelling the cosmological dependence of the covariance. Our results suggest that fixing the covariance to a fiducial cosmology can significantly affect the recovered parameter errors and that modelling the cosmological dependence of the variance while keeping the correlation coefficient fixed can alleviate the impact of this effect.

scholarly journals Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

2021 ◽  
Author(s):  
Robin E Upham ◽  
Michael L Brown ◽  
Lee Whittaker
Keyword(s):  
Power Spectrum ◽  
Random Noise ◽  
Power Spectra ◽  
Stage Iv ◽  
Wishart Distribution ◽  
Weak Lensing ◽  
Dependence Structure ◽  
Gaussian Fields ◽  
Non Gaussian ◽  
Parameter Constraints

Abstract We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from Stage IV weak lensing surveys.

scholarly journals NON-GAUSSIAN ERROR CONTRIBUTION TO LIKELIHOOD ANALYSIS OF THE MATTER POWER SPECTRUM

2010 ◽  
Vol 726 (1) ◽  
pp. 7 ◽  
Author(s):  
Ryuichi Takahashi ◽  
Naoki Yoshida ◽  
Masahiro Takada ◽  
Takahiko Matsubara ◽  
Naoshi Sugiyama ◽  
...  
Keyword(s):  
Power Spectrum ◽  
Matter Power Spectrum ◽  
Likelihood Analysis ◽  
Non Gaussian

scholarly journals Matter power spectrum: from Ly α forest to CMB scales

2019 ◽  
Vol 489 (2) ◽  
pp. 2247-2253 ◽  
Author(s):  
Solène Chabanier ◽  
Marius Millea ◽  
Nathalie Palanque-Delabrouille
Keyword(s):  
Power Spectrum ◽  
Power Spectra ◽  
Model Fit ◽  
Microwave Background ◽  
Luminous Red Galaxies ◽  
Matter Power Spectrum ◽  
Physical Scale ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Red Galaxies

ABSTRACT We present a new compilation of inferences of the linear 3D matter power spectrum at redshift $z\, {=}\, 0$ from a variety of probes spanning several orders of magnitude in physical scale and in cosmic history. We develop a new lower noise method for performing this inference from the latest Ly α forest 1D power spectrum data. We also include cosmic microwave background (CMB) temperature and polarization power spectra and lensing reconstruction data, the cosmic shear two-point correlation function, and the clustering of luminous red galaxies. We provide a Dockerized Jupyter notebook housing the fairly complex dependences for producing the plot of these data, with the hope that groups in the future can help add to it. Overall, we find qualitative agreement between the independent measurements considered here and the standard ΛCDM cosmological model fit to the Planck data.

scholarly journals Bayesian forward modelling of cosmic shear data

2021 ◽  
Vol 502 (2) ◽  
pp. 3035-3044
Author(s):  
Natalia Porqueres ◽  
Alan Heavens ◽  
Daniel Mortlock ◽  
Guilhem Lavaux
Keyword(s):  
Power Spectrum ◽  
Power Spectra ◽  
Density Field ◽  
Matter Distribution ◽  
Bayesian Hierarchical ◽  
Matter Power Spectrum ◽  
Field Samples ◽  
Dark Matter Distribution ◽  
Cosmic Shear ◽  
Non Gaussian

ABSTRACT We present a Bayesian hierarchical modelling approach to infer the cosmic matter density field, and the lensing and the matter power spectra, from cosmic shear data. This method uses a physical model of cosmic structure formation to infer physically plausible cosmic structures, which accounts for the non-Gaussian features of the gravitationally evolved matter distribution and light-cone effects. We test and validate our framework with realistic simulated shear data, demonstrating that the method recovers the unbiased matter distribution and the correct lensing and matter power spectrum. While the cosmology is fixed in this test, and the method employs a prior power spectrum, we demonstrate that the lensing results are sensitive to the true power spectrum when this differs from the prior. In this case, the density field samples are generated with a power spectrum that deviates from the prior, and the method recovers the true lensing power spectrum. The method also recovers the matter power spectrum across the sky, but as currently implemented, it cannot determine the radial power since isotropy is not imposed. In summary, our method provides physically plausible inference of the dark matter distribution from cosmic shear data, allowing us to extract information beyond the two-point statistics and exploiting the full information content of the cosmological fields.

scholarly journals Matter power spectrum covariance matrix from the DEUS-PUR ΛCDM simulations: mass resolution and non-Gaussian errors

2014 ◽  
Vol 446 (2) ◽  
pp. 1756-1764 ◽  
Author(s):  
L. Blot ◽  
P. S. Corasaniti ◽  
J.-M. Alimi ◽  
V. Reverdy ◽  
Y. Rasera
Keyword(s):  
Power Spectrum ◽  
Covariance Matrix ◽  
Mass Resolution ◽  
Matter Power Spectrum ◽  
Non Gaussian

scholarly journals Weak lensing cosmology with convolutional neural networks on noisy data

2019 ◽  
Vol 490 (2) ◽  
pp. 1843-1860 ◽  
Author(s):  
Dezső Ribli ◽  
Bálint Ármin Pataki ◽  
José Manuel Zorrilla Matilla ◽  
Daniel Hsu ◽  
Zoltán Haiman ◽  
...  
Keyword(s):  
Neural Networks ◽  
Correlation Function ◽  
Power Spectrum ◽  
Convolutional Neural Networks ◽  
Higher Order ◽  
Weak Lensing ◽  
Noise Levels ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Non Gaussian

ABSTRACT Weak gravitational lensing is one of the most promising cosmological probes of the late universe. Several large ongoing (DES, KiDS, HSC) and planned (LSST, Euclid, WFIRST) astronomical surveys attempt to collect even deeper and larger scale data on weak lensing. Due to gravitational collapse, the distribution of dark matter is non-Gaussian on small scales. However, observations are typically evaluated through the two-point correlation function of galaxy shear, which does not capture non-Gaussian features of the lensing maps. Previous studies attempted to extract non-Gaussian information from weak lensing observations through several higher order statistics such as the three-point correlation function, peak counts, or Minkowski functionals. Deep convolutional neural networks (CNN) emerged in the field of computer vision with tremendous success, and they offer a new and very promising framework to extract information from 2D or 3D astronomical data sets, confirmed by recent studies on weak lensing. We show that a CNN is able to yield significantly stricter constraints of (σ8, Ωm) cosmological parameters than the power spectrum using convergence maps generated by full N-body simulations and ray-tracing, at angular scales and shape noise levels relevant for future observations. In a scenario mimicking LSST or Euclid, the CNN yields 2.4–2.8 times smaller credible contours than the power spectrum, and 3.5–4.2 times smaller at noise levels corresponding to a deep space survey such as WFIRST. We also show that at shape noise levels achievable in future space surveys the CNN yields 1.4–2.1 times smaller contours than peak counts, a higher order statistic capable of extracting non-Gaussian information from weak lensing maps.

scholarly journals Fisher for complements: extracting cosmology and neutrino mass from the counts-in-cells PDF

2020 ◽  
Vol 495 (4) ◽  
pp. 4006-4027 ◽  
Author(s):  
Cora Uhlemann ◽  
Oliver Friedrich ◽  
Francisco Villaescusa-Navarro ◽  
Arka Banerjee ◽  
Sandrine Codis
Keyword(s):  
Power Spectrum ◽  
Neutrino Mass ◽  
Multiple Scales ◽  
Large Deviation ◽  
Matter Density ◽  
Joint Analysis ◽  
Galaxy Surveys ◽  
Matter Power Spectrum ◽  
Non Linear ◽  
In Cells

ABSTRACT We comprehensively analyse the cosmology dependence of counts-in-cells statistics. We focus on the shape of the one-point probability distribution function (PDF) of the matter density field at mildly non-linear scales. Based on large-deviation statistics, we parametrize the cosmology dependence of the matter PDF in terms of the linear power spectrum, the growth factor, the spherical collapse dynamics, and the non-linear variance. We extend our formalism to include massive neutrinos, finding that the total matter PDF is highly sensitive to the total neutrino mass Mν and can disentangle it from the clustering amplitude σ8. Using more than a million PDFs extracted from the Quijote simulations, we determine the response of the matter PDF to changing parameters in the νΛCDM model and successfully cross-validate the theoretical model and the simulation measurements. We present the first νΛCDM Fisher forecast for the matter PDF at multiple scales and redshifts, and its combination with the matter power spectrum. We establish that the matter PDF and the matter power spectrum are highly complementary at mildly non-linear scales. The matter PDF is particularly powerful for constraining the matter density Ωm, clustering amplitude σ8 and the total neutrino mass Mν. Adding the mildly non-linear matter PDF to the mildly non-linear matter power spectrum improves constraints on Ωm by a factor of 5 and σ8 by a factor of 2 when considering the three lowest redshifts. In our joint analysis of the matter PDF and matter power spectrum at three redshifts, the total neutrino mass is constrained to better than 0.01 eV with a total volume of 6 (Gpc h−1)3. We discuss how density-split statistics can be used to translate those encouraging results for the matter PDF into realistic observables in galaxy surveys.

scholarly journals Tomographic weak lensing bispectrum: a thorough analysis towards the next generation of galaxy surveys

2019 ◽  
Vol 490 (4) ◽  
pp. 4688-4714 ◽  
Author(s):  
Matteo Rizzato ◽  
Karim Benabed ◽  
Francis Bernardeau ◽  
Fabien Lacasa
Keyword(s):  
Power Spectrum ◽  
High Performance ◽  
Large Scale ◽  
Signal To Noise Ratio ◽  
Principal Component ◽  
Weak Lensing ◽  
Galaxy Surveys ◽  
Point Correlation ◽  
Non Gaussian ◽  
The Impact

ABSTRACT 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 parallelized prediction of the binned tomographic observables and of their joint non-Gaussian covariance matrix accounting for terms up to the six-point correlation function and supersample effects. This performance allows us to qualitatively address several interesting scientific questions. We find that the bispectrum provides an improvement in terms of signal-to-noise ratio (S/N) of about 10 per cent on top of the power spectrum, making it a non-negligible source of information for future surveys. Furthermore, we are capable to test the impact of theoretical uncertainties in the halo model used to build our observables; with presently allowed variations we conclude that the impact is negligible on the S/N. Finally, we consider data compression possibilities to optimize future analyses of the weak lensing bispectrum. We find that, ignoring systematics, five equipopulated redshift bins are enough to recover the information content of a Euclid-like survey, with negligible improvement when increasing to 10 bins. We also explore principal component analysis and dependence on the triangle shapes as ways to reduce the numerical complexity of the problem.

scholarly journals SEARCHING FOR DARK MATTER ISOCURVATURE INITIAL CONDITIONS WITH N-BODY SIMULATIONS

2012 ◽  
Vol 21 (03) ◽  
pp. 1250021
Author(s):  
JIE LIU
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Large Scale ◽  
Initial Conditions ◽  
Mass Function ◽  
Matter Power Spectrum ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Best Fit ◽  
Isocurvature Perturbations

Small fraction of isocurvature perturbations may exist and correlate with adiabatic perturbations in the primordial perturbations. Naively switching off isocurvature perturbations may lead to biased results. We study the effect of dark matter isocurvature on the structure formation through N-body simulations. From the best-fit values, we run four sets of simulation with different initial conditions and different box sizes. We find that, if the fraction of dark matter isocurvature is small, we cannot detect its signal through matter power spectrum and two-point correlation function with large scale survey. However, the halo mass function can give an obvious signal. Compared to 5% difference on matter power spectrum, it can get 37% at z = 3 on halo mass function. This indicates that future high precise cluster count experiment can give stringent constraints on dark matter isocurvature perturbations.

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