Log-transforming the matter power spectrum
نویسندگان
چکیده
We investigate whether non-linear effects on the large-scale power spectrum of dark matter, namely the increase in small-scale power and the smearing of baryon acoustic oscillations, can be decreased by a log-transformation or emulated by an exponential transformation of the linear spectrum. To that end we present a formalism to convert the power spectrum of a log-normal field to the power spectrum of the logarithmic Gaussian field and vice versa. All ingredients of our derivation can already be found in various publications in cosmology and other fields. We follow a more pedagogical approach providing a detailed derivation, application examples, and a discussion of implementation subtleties in one text. We use the formalism to show that the non-linear increase in small-scale power in the matter power spectrum is significantly smaller for the log-transformed spectrum which fits the linear spectrum (with less than 20% error) for redshifts down to 1 and k ≤ 1.0 h Mpc. For lower redshifts the fit to the linear spectrum is not as good, but the reduction of non-linear effects is still significant. Similarly, we show that applying the linear growth factor to the logarithmic density leads to an automatic increase in small-scale power for low redshifts fitting to third-order perturbation spectra and Cosmic Emulator spectra with an error of less than 20%. Smearing of baryon acoustic oscillations is at least three times weaker, but still present.
منابع مشابه
Rejuvenating the Matter Power Spectrum: Restoring Information with a Logarithmic Density Mapping
We find that nonlinearities in the dark-matter power spectrum are dramatically smaller if the density field first undergoes a logarithmic mapping. In the Millennium simulation, this procedure produces a power spectrum with a shape hardly departing from the linear power spectrum for k . 1hMpc−1 at all redshifts. Also, this procedure unveils pristine Fisher information on a range of scales reachi...
متن کاملTransforming Growth Factor Beta 1 869T/C and 915G/C Polymorphisms and Risk of Autism Spectrum Disorders
Background: Transforming growth factor-β1 (TGF-β1) has been found to play a crucial role in early central nervous system development. Several studies have illustrated decreased TGF-β1 levels in sera and brains of autistic children. Two point mutations in the TGF-β1 signal peptide at 869T/C and 915G/C have been reported to influence TGF-β1 expression. The aim of the pres...
متن کاملApplication of spectrum-volume fractal modeling for detection of mineralized zones
The main goal of this research work was to detect the different Cu mineralized zones in the Sungun porphyry deposit in NW Iran using the Spectrum-Volume (S-V) fractal modeling based on the sub-surface data for this deposit. This operation was carried out on an estimated Cu block model based on a Fast Fourier Transformation (FFT) using the C++ and MATLAB programing. The S-V log-log plot was gene...
متن کاملA New RSTB Invariant Image Template Matching Based on Log-Spectrum and Modified ICA
Template matching is a widely used technique in many of image processing and machine vision applications. In this paper we propose a new as well as a fast and reliable template matching algorithm which is invariant to Rotation, Scale, Translation and Brightness (RSTB) changes. For this purpose, we adopt the idea of ring projection transform (RPT) of image. In the proposed algorithm, two novel s...
متن کاملProbing the Intergalactic Medium with the Lyα forest along multiple lines of sight to distant QSOs
We present an effective implementation of analytical calculations of the Lyα opacity distribution of the Intergalactic Medium (IGM) along multiple lines of sight (LOS) to distant quasars in a cosmological setting. The method assumes that the distribution of neutral hydrogen follows that of an underlying dark matter density field and that the density distribution is a (local) lognormal distribut...
متن کامل