scholarly journals Higher order spectra of weak lensing convergence maps in parametrized theories of modified gravity

2020 ◽  
Vol 498 (4) ◽  
pp. 5299-5316
Author(s):  
D Munshi ◽  
J D McEwen

ABSTRACT We compute the low-ℓ limit of the family of higher order spectra for projected (2D) weak lensing convergence maps. In this limit these spectra are computed to an arbitrary order using tree-level perturbative calculations. We use the flat-sky approximation and Eulerian perturbative results based on a generating function approach. We test these results for the lower order members of this family, i.e. the skew- and kurt-spectra against state-of-the-art simulated all-sky weak lensing convergence maps and find our results to be in very good agreement. We also show how these spectra can be computed in the presence of a realistic sky-mask and Gaussian noise. We generalize these results to 3D and compute the equal-time higher order spectra. These results will be valuable in analysing higher order statistics from future all-sky weak lensing surveys such as the Euclid survey at low-ℓ modes. As illustrative examples, we compute these statistics in the context of the Horndeski and beyond Horndeski theories of modified gravity. They will be especially useful in constraining theories such as the Gleyzes–Langlois–Piazza–Vernizzi (GLPV) theories and degenerate higher order scalar-tensor theories as well as the commonly used normal-branch of Dvali–Gabadadze–Porrati model, clustering quintessence models and scenarios with massive neutrinos.

2018 ◽  
Vol 619 ◽  
pp. A38 ◽  
Author(s):  
Austin Peel ◽  
Valeria Pettorino ◽  
Carlo Giocoli ◽  
Jean-Luc Starck ◽  
Marco Baldi

General relativity (GR) has been well tested up to solar system scales, but it is much less certain that standard gravity remains an accurate description on the largest, that is cosmological, scales. Many extensions to GR have been studied that are not yet ruled out by the data, including by that of the recent direct gravitational wave detections. Degeneracies among the standard model (ΛCDM) and modified gravity (MG) models, as well as among different MG parameters, must be addressed in order to best exploit information from current and future surveys and to unveil the nature of dark energy. We propose various higher-order statistics in the weak-lensing signal as a new set of observables able to break degeneracies between massive neutrinos and MG parameters. We have tested our methodology on so-called f(R) models, which constitute a class of viable models that can explain the accelerated universal expansion by a modification of the fundamental gravitational interaction. We have explored a range of these models that still fit current observations at the background and linear level, and we show using numerical simulations that certain models which include massive neutrinos are able to mimic ΛCDM in terms of the 3D power spectrum of matter density fluctuations. We find that depending on the redshift and angular scale of observation, non-Gaussian information accessed by higher-order weak-lensing statistics can be used to break the degeneracy between f(R) models and ΛCDM. In particular, peak counts computed in aperture mass maps outperform third- and fourth-order moments.


1975 ◽  
Vol 72 (4) ◽  
pp. 673-694 ◽  
Author(s):  
C. W. Van Atta ◽  
J. C. Wyngaard

Measurements of higher-order spectra of turbulent velocity fluctuations in the atmospheric boundary layer over the open ocean and land produce the interesting result that, in the wavenumber range designated originally by Kolmogorov as an inertial subrange, the functional dependence of the spectra on wavenumber is practically independent of the order of the spectrum. These results confirm the observation of Dutton & Deaven that their extension by a dimensional similarity argument of the original Kolmogorov theory to higher-order spectra was not valid. In the present work, we derive an alternative generalization of the Kolmogorov ideas for spectra of arbitrary order. The results of this generalization describe the dependence upon wavenumber of the available data quite well. We also present theoretical calculations based on a Gaussian model for the fluctuating velocity field which furnish quantitative predictions for spectra of arbitrary order that are also in good agreement with the measurements, both in functional form and in absolute value.Comparison of results based on the Gaussian model with laboratory measurements obtained in a free shear layer shows that the Gaussian theory predicts accurately all the available normalized higher-order spectra for all frequencies. When the corresponding measured higher-order moments are close to those expected for a Gaussian process, the Gaussian theory also correctly predicts the absolute magnitudes of the higher-order spectra.


1989 ◽  
Vol 04 (21) ◽  
pp. 2063-2071
Author(s):  
GEORGE SIOPSIS

It is shown that the contact term discovered by Wendt is sufficient to ensure finiteness of all tree-level scattering amplitudes in Witten’s field theory of open superstrings. Its inclusion in the action also leads to a gauge-invariant theory. Thus, no additional higher-order counterterms in the action are needed.


2011 ◽  
Vol 403-408 ◽  
pp. 4859-4866 ◽  
Author(s):  
Saptarshi Das ◽  
Amitava Gupta ◽  
Shantanu Das

Generalization of the frequency domain robust tuning has been proposed in this paper for a family of fractional order (FO) PI/PID controllers. The controller tuning is enhanced with two new FO reduced parameter templates which are capable of capturing higher order process dynamics with much better accuracy. The paper validates the proposed methodology with a standard test-bench of higher order processes to show the relative merits of the family of FO controller structures.


2006 ◽  
Author(s):  
Jeongmok Cho ◽  
Taegeun Jung ◽  
Dong-Hyeon Kim ◽  
Nam Huh ◽  
Tae-Whee Joung ◽  
...  

2009 ◽  
Vol 33 (1) ◽  
pp. 42-50 ◽  
Author(s):  
K. C. Chua ◽  
V. Chandran ◽  
U. Rajendra Acharya ◽  
C. M. Lim

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