Model-independent versus model-dependent interpretation of the SDSS-III BOSS power spectrum: Bridging the divide

Abstract In the standard (classic) approach, galaxy clustering measurements from spectroscopic surveys are compressed into baryon acoustic oscillations and redshift space distortions measurements, which in turn can be compared to cosmological models. Recent works have shown that avoiding this intermediate step and fitting directly the full power spectrum signal (full modelling) leads to much tighter constraints on cosmological parameters. Here we show where this extra information is coming from and extend the classic approach with one additional effective parameter, such that it captures, effectively, the same amount of information as the full modelling approach, but in a model-independent way. We validate this new method (ShapeFit) on mock catalogs, and compare its performance to the full modelling approach finding both to deliver equivalent results. The ShapeFit extension of the classic approach promotes the standard analyses at the level of full modelling ones in terms of information content, with the advantages of i) being more model independent; ii) offering an understanding of the origin of the extra cosmological information; iii) allowing a robust control on the impact of observational systematics.

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Model independent foreground power spectrum estimation using WMAP 5-year data

Physical Review D ◽

10.1103/physrevd.79.123011 ◽

2009 ◽

Vol 79 (12) ◽

Cited By ~ 3

Author(s):

Tuhin Ghosh ◽

Rajib Saha ◽

Pankaj Jain ◽

Tarun Souradeep

Keyword(s):

Power Spectrum ◽

Spectrum Estimation ◽

Power Spectrum Estimation ◽

Model Independent

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Model‐independent Primordial Power Spectrum from MAXIMA, BOOMERANG, and DASI Data

The Astrophysical Journal ◽

10.1086/340492 ◽

2002 ◽

Vol 573 (1) ◽

pp. 1-6 ◽

Cited By ~ 26

Author(s):

Yun Wang ◽

Grant J. Mathews

Keyword(s):

Power Spectrum ◽

Primordial Power Spectrum ◽

Model Independent

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Measuring the Hubble function with standard candle clustering

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab887 ◽

2021 ◽

Author(s):

Luca Amendola ◽

Miguel Quartin

Keyword(s):

Dark Energy ◽

Equation Of State ◽

Power Spectrum ◽

Energy Equation ◽

Luminosity Distance ◽

Distortion Parameter ◽

Peculiar Velocities ◽

Matter Power Spectrum ◽

Standard Candle ◽

Model Independent

Abstract Supernova Ia magnitude surveys measure the dimensionless luminosity distance H0DL. However, from the distances alone one cannot obtain quantities like H(z) or the dark energy equation of state, unless further cosmological assumptions are imposed. Here we show that by measuring the power spectrum of density contrast and of peculiar velocities of supernovae one can estimate also H(z)/H0 regardless of background or linearly perturbed cosmology and of galaxy-matter bias. This method, dubbed Clustering of Standard Candles (CSC) also yields the redshift distortion parameter β(k, z) and the biased matter power spectrum in a model-independent way. We forecast that an optimistic (pessimistic) LSST may be able to constrain H(z)/H0 to 5–13% (9–40%) in redshift bins of Δz = 0.1 up to at least z = 0.6.

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

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100112713 ◽

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.

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Log-log scale roughness spectroscopy of surfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100146965 ◽

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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