scholarly journals Joint analysis of anisotropic power spectrum, bispectrum and trispectrum: application to N-body simulations

2021 ◽  
Vol 2021 (07) ◽  
pp. 008
Author(s):  
Davide Gualdi ◽  
Héctor Gil-Marín ◽  
Licia Verde
Keyword(s):  
Power Spectrum ◽  
Joint Analysis

Cosmic Data Fusion

2005 ◽  
Vol 201 ◽  
pp. 368-376
Author(s):  
S. L. Bridle
Keyword(s):  
Power Spectrum ◽  
Large Scale ◽  
Cosmological Parameters ◽  
Big Bang ◽  
Joint Analysis ◽  
Data Sets ◽  
Cluster Number ◽  
Scale Invariant ◽  
Peculiar Velocities ◽  
Initial Power

We compare and combine likelihood functions of the cosmological parameters Ωm, h and σ8 from the CMB, type Ia supernovae and from probes of large scale structure. We include the recent results from the CMB experiments BOOMERANG and MAXIMA-1. Our analysis assumes a flat ACDM cosmology with a scale-invariant adiabatic initial power spectrum. First we consider three data sets that directly probe the mass in the Universe, without the need to relate the galaxy distribution to the underlying mass via a “biasing” relation: peculiar velocities, CMB and supernovae. We assume a baryonic fraction as inferred from Big-Bang Nucleosynthesis and find that all three data sets agree well, overlapping significantly at the 2σ level. This therefore justifies a joint analysis, in which we find a joint best fit point and 95% confidence limits of Ωm = 0.28 (0.17, 0.39), h = 0.74 (0.64, 0.86), and σ8 = 1.17 (0.98,1.37). Secondly we extend our earlier work on combining CMB, supernovae, cluster number counts, IRAS galaxy redshift survey data to include BOOMERANG and MAXIMA-1 data and to allow a free Ωbh2. We find that, given our assumption of a scale invariant initial power spectrum (n = 1), we obtain the robust result of Ωbh2 = 0.031 ± 0.03, which is dominated by the CMB constraint.

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 Cross-correlation between cosmological and astrophysical datasets: the Planck and Herschel case

2014 ◽  
Vol 10 (S306) ◽  
pp. 202-205 ◽  
Author(s):  
Federico Bianchini ◽  
Andrea Lapi
Keyword(s):  
Power Spectrum ◽  
Cross Correlation ◽  
Forthcoming Paper ◽  
Joint Analysis ◽  
Atlas Data ◽  
Λcdm Model ◽  
The Galaxy ◽  
The Cross ◽  
Galaxy Bias ◽  
Cross Power Spectrum

AbstractWe present the first measurement of the correlation between the map of the CMB lensing potential derived from the Planck nominal mission data and z ≳ 1.5 galaxies detected by Herschel-ATLAS (H-ATLAS) survey covering about 550 deg2. We detect the cross-power spectrum with a significance of ∼ 8.5σ, ruling out the absence of correlation at 9σ. We check detection with a number of null tests. The amplitude of cross-correlation and the galaxy bias are estimated using joint analysis of the cross-power spectrum and the galaxy survey auto-spectrum, which allows to break degeneracy between these parameters. The estimated galaxy bias is consistent with previous estimates of the bias for the H-ATLAS data, while the cross-correlation amplitude is higher than expected for a ΛCDM model. The content of this work is to appear in a forthcoming paper Bianchini, et al. (2014).

scholarly journals Primordial non-Gaussianity without tails – how to measure fNL with the bulk of the density PDF

2020 ◽  
Vol 498 (1) ◽  
pp. 464-483 ◽  
Author(s):  
Oliver Friedrich ◽  
Cora Uhlemann ◽  
Francisco Villaescusa-Navarro ◽  
Tobias Baldauf ◽  
Marc Manera ◽  
...  
Keyword(s):  
Power Spectrum ◽  
Initial Conditions ◽  
Density Fluctuations ◽  
Joint Analysis ◽  
Late Time ◽  
Non Linear ◽  
Free Parameters ◽  
Non Gaussian ◽  
The Impact ◽  
Time Density

ABSTRACT We investigate the possibility to detect primordial non-Gaussianity by analysing the bulk of the probability distribution function (PDF) of late-time cosmic density fluctuations. For this purpose, we devise a new method to predict the impact of general non-Gaussian initial conditions on the late-time density PDF. At redshift z = 1 and for a smoothing scale of 30 Mpc h−1 our predictions agree with the high-resolution Quijote N-body simulations to $\sim 0.2{{\ \rm per\ cent}}$ precision. This is within cosmic variance of a ∼100(Gpc h−1)3 survey volume. When restricting to this 30 Mpc h−1 smoothing scale and to mildly non-linear densities (δ[30 Mpc h−1] ∈ [−0.3, 0.4]) and also marginalizing over potential ignorance of the amplitude of the non-linear power spectrum an analysis of the PDF for such a survey volume can still measure the amplitude of different primordial bispectrum shapes to an accuracy of $\Delta f_{\mathrm{NL}}^{\mathrm{loc}} = \pm 7.4\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{equi}} = \pm 22.0\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{ortho}} = \pm 46.0$. When pushing to smaller scales and assuming a joint analysis of the PDF with smoothing radii of 30 and 15 Mpc h−1 (δ[15 Mpc h−1] ∈ [−0.4, 0.5]) this improves to $\Delta f_{\mathrm{NL}}^{\mathrm{loc}} = \pm 3.3\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{equi}} = \pm 11.0\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{ortho}} = \pm 17.0$ – even when marginalizing over the non-linear variances at both scales as two free parameters. Especially, such an analysis could simultaneously measure fNL and the amplitude and slope of the non-linear power spectrum. However, at 15 Mpc h−1 our predictions are only accurate to $\lesssim 0.8{{\ \rm per\ cent}}$ for the considered density range. We discuss how this has to be improved in order to push to these small scales and make full use of upcoming surveys with a PDF-based analysis.

scholarly journals Testing one-loop galaxy bias: Joint analysis of power spectrum and bispectrum

2021 ◽  
Vol 103 (12) ◽  
Author(s):  
Alexander Eggemeier ◽  
Román Scoccimarro ◽  
Robert E. Smith ◽  
Martin Crocce ◽  
Andrea Pezzotta ◽  
...  
Keyword(s):  
Power Spectrum ◽  
Joint Analysis ◽  
Galaxy Bias

scholarly journals Isocurvature modes: joint analysis of the CMB power spectrum and bispectrum

2021 ◽  
Vol 2021 (01) ◽  
pp. 004-004
Author(s):  
T. Montandon ◽  
G. Patanchon ◽  
B. van Tent
Keyword(s):  
Power Spectrum ◽  
Joint Analysis

The on-line use of histogram data for high-speed correction and alignment of electron microscope images

1984 ◽  
Vol 42 ◽  
pp. 556-557
Author(s):  
William Krakow
Keyword(s):  
Power Spectrum ◽  
High Speed ◽  
Direct Memory Access ◽  
Digital Television ◽  
Contrast Transfer Function ◽  
The Past ◽  
High Resolution Tem ◽  
On Line ◽  
Correction Of Astigmatism ◽  
The Fourier Transform

In the past few years on-line digital television frame store devices coupled to computers have been employed to attempt to measure the microscope parameters of defocus and astigmatism. The ultimate goal of such tasks is to fully adjust the operating parameters of the microscope and obtain an optimum image for viewing in terms of its information content. The initial approach to this problem, for high resolution TEM imaging, was to obtain the power spectrum from the Fourier transform of an image, find the contrast transfer function oscillation maxima, and subsequently correct the image. This technique requires a fast computer, a direct memory access device and even an array processor to accomplish these tasks on limited size arrays in a few seconds per image. It is not clear that the power spectrum could be used for more than defocus correction since the correction of astigmatism is a formidable problem of pattern recognition.

Log-log scale roughness spectroscopy of surfaces

1993 ◽  
Vol 51 ◽  
pp. 224-225
Author(s):  
P. Fraundorf ◽  
B. Armbruster
Keyword(s):  
Power Spectrum ◽  
Autocorrelation Function ◽  
Power Spectra ◽  
Scanning Force Microscopy ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Force Microscopy ◽  
Scanning Force ◽  
Lateral Structure ◽  
Scale Roughness

Optical interferometry, confocal light microscopy, stereopair scanning electron microscopy, scanning tunneling microscopy, and scanning force microscopy, can produce topographic images of surfaces on size scales reaching from centimeters to Angstroms. Second moment (height variance) statistics of surface topography can be very helpful in quantifying “visually suggested” differences from one surface to the next. The two most common methods for displaying this information are the Fourier power spectrum and its direct space transform, the autocorrelation function or interferogram. Unfortunately, for a surface exhibiting lateral structure over several orders of magnitude in size, both the power spectrum and the autocorrelation function will find most of the information they contain pressed into the plot’s origin. This suggests that we plot power in units of LOG(frequency)≡-LOG(period), but rather than add this logarithmic constraint as another element of abstraction to the analysis of power spectra, we further recommend a shift in paradigm.

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