We develop a theoretical formula to incorporate the window effect into the multipole power spectra for the first time. In the first half of the present paper, we consider the convolved power spectrum. The convolved power spectrum includes the effect of the window function. Thus, it must be properly taken into account when comparing the observational data with theoretical predictions. In this case, the effect of the window function is crucial as we will show in the present paper.
#Redshift window functions full
In this method, a full sample of a wide survey area is divided into smaller subsamples with equal areas. In the present paper, we consider different estimators of the quadrupole power spectrum which allows the use of the FFT. However, the disadvantage of the method is not being compatible with the use of the fast Fourier transform (FFT). An estimator of the quadrupole power spectrum is developed in Ref. The usefulness of the quadrupole power spectrum to constrain modified gravity models is demonstrated in Refs. The multipole power spectrum is useful for measuring the redshift-space distortion. In these analyses, measuring the multiple power spectrum in the distribution of galaxies plays a key role (cf. The measurement of the Kaiser effect is thought to be useful for testing the general relativity and other modified gravity theories. It is caused by the bulk motion of galaxies. The Kaiser effect is the redshift-space distortion in the linear regime of the density perturbations. Also, the spatial distribution of galaxies is distorted due to the peculiar motions, which is called the redshift-space distortion. Here, a measurement of the baryon acoustic oscillations in the galaxy distribution plays a key role. Galaxy redshift surveys provide promising ways of measuring the dark energy properties. A key for distinguishing between the dark energy and modified gravity theory is a measurement of the evolution of cosmological perturbations. These surveys provide us with a chance to test the hypothetical dark energy, as well as the gravity theory on the scales of cosmology. Dark energy surveys which aim at measuring redshifts of huge number of galaxies are in progress or planned. In either case, this problem seems to be deeply rooted in the nature of fundamental physics, which has attracted many researchers. Modification of the gravity theory is an alternative way to explain it. A hypothetical energy component, dark energy, may explain the accelerated expansion. One of the most fundamental problems in cosmology is the origin of an accelerated expansion of the Universe.
#Redshift window functions how to
We demonstrate how to deal with the window effect in these two approaches, applying them to the Sloan Digital Sky Survey (SDSS) luminous red galaxy (LRG) sample. In the second approach, we measure the multipole power spectrum deconvolved from the window effect. Second, we investigate the deconvolved power spectrum, which is obtained by using the Fourier deconvolution theorem.
We show how the convolved multipole power spectrum is related to the original power spectrum, using the multipole moments of the window function. First, we consider the convolved power spectrum including the window effect, which is obtained by following the familiar (FKP) method developed by Feldman, Kaiser and Peacock. We investigate the effect of the window function on the multipole power spectrum in two different ways. Keywords: Cosmology Large-Scale Structure of Universe Received Jrevised Augaccepted August 16, 2013 This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1Graduate School of Physical Sciences, Hiroshima University, Higashi-Hiroshima, JapanĮmail: © 2013 Takahiro Sato et al.
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