Galaxy Power Spectrum In Redshift Space Research Articles

FkPT: constraining scale-dependent modified gravity with the full-shape galaxy power spectrum

Modified gravity models with scale-dependent linear growth typically exhibit an enhancement in the power spectrum beyond a certain scale. The conventional methods for extracting cosmological information usually involve inferring modified gravity effects via Redshift Space Distortions (RSD), particularly through the time evolution of fσ 8. However, classical galaxy RSD clustering analyses encounter difficulties in accurately capturing the spectrum's enhanced power, which is better obtained from the broad-band power spectrum. In this sense, full-shape analyses aim to consider survey data using comprehensive and precise models of the whole power spectrum. Yet, a major challenge in this approach is the slow computation of non-linear loop integrals for scale-dependent modified gravity, precluding the estimation of cosmological parameters using Markov Chain Monte Carlo methods. Based on recent studies, in this work we develop a perturbation theory tailored for Modified Gravity, or analogous scenarios introducing additional scales, such as in the presence of massive neutrinos. Our approach only needs the calculation of the scale-dependent growth rate f(k,t) and the limit of the perturbative kernels at large scales. We called this approximate technique as fk-Perturbation Theory and implemented it into the code fkpt, capable of computing the redshift space galaxy power spectrum in a fraction of a second. We validate our modeling and code with the f(R) theory MG-GLAM and General Relativity NSeries sets of simulations. The code is available at https://github.com/alejandroaviles/fkpt.

Fast computation of non-linear power spectrum in cosmologies with massive neutrinos

We compute 1-loop corrections to the redshift space galaxy power spectrum in cosmologies containing additional scales, and hence kernels different from Einstein-de Sitter (EdS). Specifically, our method is tailored for cosmologies in the presence of massive neutrinos and some modified gravity models; in this article we concentrate on the former case. The perturbative kernels have contributions that we notice appear either from the logarithmic growth rate f(k,t), which is scale-dependent because of the neutrino free-streaming, or from the failure of the commonly used approximation f 2 = Ω m . The latter contributions make the computation of loop corrections quite slow, precluding full-shape analyses for parameter estimation. However, we identify that the dominant pieces of the kernels come from the growth factor, allowing us to simplify the kernels but retaining the characteristic free-streaming scale introduced by the neutrinos' mass. Moreover, with this simplification one can exploit FFTLog methods to speed up the computations even more. We validate our analytical modeling and numerical method with halo catalogs extracted from the Quijote simulations finding good agreement with the, a priori, known cosmological parameters. We make public our Python code FOLPSν to compute the redshift space power spectrum in a fraction of second. Code available at https://github.com/henoriega/FOLPS-nu.

Neural network acceleration of large-scale structure theory calculations

We make use of neural networks to accelerate the calculation of power spectra required for the analysis of galaxy clustering and weak gravitational lensing data. For modern perturbation theory codes, evaluation time for a single cosmology and redshift can take on the order of two seconds. In combination with the comparable time required to compute linear predictions using a Boltzmann solver, these calculations are the bottleneck for many contemporary large-scale structure analyses. In this work, we construct neural network-based surrogate models for Lagrangian perturbation theory (LPT) predictions of matter power spectra, real and redshift space galaxy power spectra, and galaxy-matter cross power spectra that attain ∼ 0.1% (at one sigma) accuracy over a broad range of scales in a ωCDM parameter space. The neural network surrogates can be evaluated in approximately one millisecond, a factor of 1000 times faster than the full Boltzmann code and LPT computations. In a simulated full-shape redshift space galaxy power spectrum analysis, we demonstrate that the posteriors obtained using our surrogates are accurate compared to those obtained using the full LPT model. We make our surrogate models public at https://github.com/sfschen/EmulateLSS, so that others may take advantage of the speed gains they provide to enable rapid iteration on analysis settings, something that is essential in complex contemporary large-scale structure analyses.

Blinded challenge for precision cosmology with large-scale structure: Results from effective field theory for the redshift-space galaxy power spectrum

An accurate theoretical template for the galaxy power spectrum is key for the success of ongoing and future spectroscopic surveys. We examine to what extent the effective field theory (EFT) of large-scale structure is able to provide such a template and correctly estimate cosmological parameters. To that end, we initiate a blinded challenge to infer cosmological parameters from the redshift-space power spectrum of high-resolution mock catalogs mimicking the BOSS galaxy sample but covering a 100 times larger cumulative volume. This gigantic simulation volume allows us to separate systematic bias due to theoretical modeling from the statistical error due to sample variance. The challenge is to measure three unknown input parameters used in the simulation: the Hubble constant, the matter density fraction, and the clustering amplitude. We present analyses done by two independent teams, who have fitted the mock simulation data generated by yet another independent group. This allows us to avoid any confirmation bias by analyzers and to pin down possible tuning of the specific EFT implementations. Both independent teams have recovered the true values of the input parameters within subpercent statistical errors corresponding to the total simulation volume.

Local Primordial Non-Gaussianities and super-sample variance

Fluctuations with wavelengths larger than the volume of a galaxy survey affect the measurement of the galaxy power spectrum within the survey itself. In the presence of local Primordial Non-Gaussianities (PNG), in addition to super-sample matter density and tidal fluctuations, the large-scale gravitational potential also induces a modulation of the observed power spectrum. In this work we investigate this modulation by computing for the first time the response of the redshift-space galaxy power spectrum to the presence of a long wavelength gravitational potential, fully accounting for the stochastic contributions. For biased tracers new response functions arise due to couplings between the small-scale fluctuations in the density, velocity and gravitational fields, the latter through scale dependent bias operators, and the large-scale gravitational potential. We study the impact of the super-sample modes on the measurement of the amplitude of the primordial bispectrum of the local-shape, fNLloc, accounting for modulations of both the signal and the covariance of the galaxy power spectrum by the long modes. Considering DESI-like survey specifications, we show that in most cases super-sample modes cause little or no degradation of the constraints, and could actually reduce the errorbars on fNLloc by (10–30)%, if external information on the bias parameters is available.

Accurate emulator for the redshift-space power spectrum of dark matter halos and its application to galaxy power spectrum

An accurate theoretical template of the redshift-space galaxy power spectrum, if applicable out to nonlinear scales, enables us to extract more stringent and robust constraints on cosmological parameters from the measured galaxy clustering. In this work, we develop a simulation-based template, so-called emulator, for the redshift-space power spectrum of dark matter halos. Using the redshift-space halo power spectra measured from the Dark Quest $N$-body simulation suite that covers 101 flat-geometry $w$CDM cosmologies around the Planck $\Lambda$CDM model, we feed these data into a feed-forward neural network to build the fast and accurate emulation of the power spectrum from the linear to nonlinear scales up to $k \simeq 0.6 \,h \,{\rm Mpc}^{-1}$. Our emulator achieves about 1% and 5% fractional accuracies in predicting the monopole and quadrupole moments of the power spectrum, respectively, for halos of $\sim 10^{13}h^{-1}M_\odot$ that correspond to host halos of the SDSS LOWZ- and CMASS-like galaxies, where the achieved accuracies are sufficient compared to the statistical errors of SDSS volume. The validation and performance of the emulator are given by the comparison of the emulator predictions with the power spectra directly measured from the simulations for validation sets that are not used in the training. We demonstrate that the emulator outputs can be used to make model predictions for the redshift-space power spectrum of galaxies by employing user-fed models for the halo-galaxy connection, such as the halo occupation distribution. The emulator allows us to easily incorporate the Finger-of-God effect due to the virial motions of galaxies and the Alcock-Paczy\'{n}ski distortions. Our code can compute the redshift-space galaxy power spectrum in a CPU subseconds and is ready to perform the emulator-based cosmological analysis for the exiting and upcoming galaxy redshift surveys.

Fast calculation of the nonlinear redshift-space galaxy power spectrum including selection bias

We present a fast implementation of the next-to-leading order (1-loop) redshift-space galaxy power spectrum by using FFTlog-based methods. [V. Desjacques, D. Jeong, and F. Schmidt, JCAP 1812 (12), 035] have shown that the 1-loop galaxy power spectrum in redshift space can be computed with 28 independent loop integrals with 22 bias parameters. Analytical calculation of the angular part of the loop integrals leaves the radial part in the form of a spherical Bessel transformation that is ready to be integrated numerically by using the FFTLog transformation. We find that the original 28 loop integrals can be solved with a total of 85 unique FFTLog transformations, yet leading to a few orders of magnitude speed up over traditional multi-dimensional integration. The code used in this work is publicly available at https://github.com/JosephTomlinson/GeneralBiasPk

Cosmological parameters and neutrino masses from the final Planck and full-shape BOSS data

We present a joint analysis of the Planck cosmic microwave background (CMB) and Baryon Oscillation Spectroscopic Survey (BOSS) final data releases. A key novelty of our study is the use of a new full-shape (FS) likelihood for the redshift-space galaxy power spectrum of the BOSS data, based on an improved perturbation theory template. We show that the addition of the redshift space galaxy clustering measurements breaks degeneracies present in the CMB data alone and tightens constraints on cosmological parameters. Assuming the minimal $\Lambda$CDM cosmology with massive neutrinos, we find the following late-Universe parameters: the Hubble constant \mbox{$H_0=67.95^{+0.66}_{-0.52}$ km s$^{-1}$Mpc$^{-1}$}, the matter density fraction \mbox{$\Omega_m=0.3079^{+0.0065}_{-0.0085}\,$}, the mass fluctuation amplitude \mbox{$\sigma_8=0.8087_{-0.0072}^{+0.012}\,$}, and an upper limit on the sum of neutrino masses \mbox{$M_{\text{tot}} <0.16\,$ eV} ($95\%$ CL).This can be contrasted with the Planck-only measurements: \mbox{$H_0=67.14_{-0.72}^{+1.3}$} km s$^{-1}$Mpc$^{-1}$, $\Omega_m=0.3188^{+0.0091}_{-0.016}\,$, \mbox{$\sigma_8=0.8053_{-0.0091}^{+0.019}\,$}, and \mbox{$M_{\text{tot}} <0.26\,$ eV} ($95\%$ CL). Our bound on the sum of neutrino masses relaxes once the hierarchy-dependent priors from the oscillation experiments are imposed. The addition of the new FS likelihood also constrains the effective number of extra relativistic degrees of freedom, \mbox{$N_{\text{eff}}=2.88\pm 0.17$}. Our study shows that the current FS and the pure baryon acoustic oscillation data add a similar amount of information in combination with the Planck likelihood. We argue that this is just a coincidence given the BOSS volume and efficiency of the current reconstruction algorithms.In the era of future surveys FS will play a dominant role in cosmological parameter measurements.

Neutrino mass and dark energy constraints from redshift-space distortions

Cosmology in the near future promises a measurement of the sum of neutrino masses ∑ mν, a fundamental Standard Model parameter, as well as substantially-improved constraints on the dark energy. We use the shape of the BOSS redshift-space galaxy power spectrum, in combination with CMB and supernova data, to constrain the neutrino masses and the dark energy. Essential to this calculation are several recent advances in non-linear cosmological perturbation theory, including fast Fourier transform methods, redshift space distortions, and scale-dependent growth. Our 95% confidence upper bound ∑ mν < 180 meV degrades substantially to ∑ mν < 540 meV when the dark energy equation of state and its first derivative are also allowed to vary, representing a significant challenge to current constraints. We also study the impact of additional galaxy bias parameters, finding that a greater allowed range of scale-dependent bias only slightly shifts the preferred ∑ mν, weakens its upper bound by ≈ 20%, and has a negligible effect on the other cosmological parameters.

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: a tomographic measurement of structure growth and expansion rate from anisotropic galaxy clustering in Fourier space

We perform a tomographic structure growth and expansion rate analysis using the monopole, quadrupole and hexadecapole of the redshift-space galaxy power spectrum derived from the Sloan Digital Sky Survey (SDSS-III) Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 combined sample, which covers the redshift range of $0.20<z<0.75$. By allowing for overlap between neighbouring redshift slices in order to extract information on the light-cone, we successfully obtain joint BAO and RSD constraints with a precision of $2-3\%$ for $D_A$, $3-10\%$ for $H$ and $9-12\%$ for $f\sigma_8$ with a redshift resolution of $\Delta z\sim0.04$. Our measurement is consistent with that presented in arXiv:1709.05173, where the analysis is performed in configuration space. We apply our measurement to constrain the $f(R)$ gravity model, and find that the 95\% CL upper limit of ${\rm log_{10}}B_0$ can be reduced by 11\% by our tomographic BAO and RSD measurement.

Maximal compression of the redshift-space galaxy power spectrum and bispectrum

We explore two methods of compressing the redshift space galaxy power spectrum and bispectrum with respect to a chosen set of cosmological parameters. Both methods involve reducing the dimension of the original data-vector ( e.g. 1000 elements ) to the number of cosmological parameters considered ( e.g. seven ) using the Karhunen-Lo\`eve algorithm. In the first case, we run MCMC sampling on the compressed data-vector in order to recover the one-dimensional (1D) and two-dimensional (2D) posterior distributions. The second option, approximately 2000 times faster, works by orthogonalising the parameter space through diagonalisation of the Fisher information matrix before the compression, obtaining the posterior distributions without the need of MCMC sampling. Using these methods for future spectroscopic redshift surveys like DESI, EUCLID and PFS would drastically reduce the number of simulations needed to compute accurate covariance matrices with minimal loss of constraining power. We consider a redshift bin of a DESI-like experiment. Using the power spectrum combined with the bispectrum as a data-vector, both compression methods on average recover the 68% credible regions to within 0.7% and 2% of those resulting from standard MCMC sampling respectively. These confidence intervals are also smaller than the ones obtained using only the power spectrum by (81%, 80%, 82%) respectively for the bias parameter b_1, the growth rate f and the scalar amplitude parameter A_s.

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: tomographic BAO analysis of DR12 combined sample in Fourier space

We perform a tomographic baryon acoustic oscillations (BAO) analysis using the monopole, quadrupole and hexadecapole of the redshift-space galaxy power spectrum measured from the pre-reconstructed combined galaxy sample of the completed Sloan Digital Sky Survey (SDSS-III) Baryon Oscillation Spectroscopic Survey (BOSS) Data Release (DR)12 covering the redshift range of $0.20<z<0.75$. By allowing for overlap between neighbouring redshift slices, we successfully obtained the isotropic and anisotropic BAO distance measurements within nine redshift slices to a precision of $1.5\%-3.4\%$ for $D_V/r_d$, $1.8\% -4.2\%$ for $D_A/r_d$ and $3.7\% - 7.5\%$ for $H \ r_d$, depending on effective redshifts. We provide our BAO measurement of $D_A/r_d$ and $H \ r_d$ with the full covariance matrix, which can be used for cosmological implications. Our measurements are consistent with those presented in \citet{Acacia}, in which the BAO distances are measured at three effective redshifts. We constrain dark energy parameters using our measurements, and find an improvement of the Figure-of-Merit of dark energy in general due to the temporal BAO information resolved. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS.

Effect of relative velocity and density perturbations between baryons and dark matter on the clustering of galaxies

Pre-recombination acoustic oscillations induce non-adiabatic perturbations between baryons and dark matter, corresponding to a constant relative-density $\delta_{bc}$ and decaying relative-velocity perturbation $\vec{v}_{bc}$. Due to their significant large-scale correlations and prominent baryon acoustic oscillation (BAO) features, these modes are potentially important for the use of the BAO as standard ruler. We present a complete treatment of the effects of the baryon-CDM perturbations on galaxy clustering in the context of a rigorous perturbative bias expansion. The leading effects are proportional to $\delta_{bc}$ and $\theta_{bc} = \partial_i v_{bc}^i$. We estimate the magnitude of these terms through the excursion set approach. The contribution from $v_{bc}^2$, which has attracted significant attention recently, contributes at subleading (1-loop) order. The relative-density contribution $\delta_{bc}$ is expected to be by far the largest contribution. We also point out contributions to the galaxy velocity bias, the largest of which is simply $v_{bc}$, leading to a term $\propto \mu^2\theta_{bc}$ in the redshift-space galaxy power spectrum $P_g^s(k,\mu)$. Complete expressions of the galaxy power spectrum at 1-loop order are given, which contain several new terms.

The Power Spectrum of the CfA/SSRS UZC Galaxy Redshift Survey

The combined CfA2/SSRS redshift catalog has recently been improved and made public. We compute the redshift-space power spectrum of this catalog using the regions at -2.5 < delta < 50 north (8h < alpha < 17h) and south (20h < alpha < 3h, b < -13) of the Galactic plane, where it is 98% complete down to Zwicky magnitude 15.5 and contains 13,681 galaxies. Our analysis uses Heavens-Taylor mode expansion, Karhunen-Loeve data compression and the Fisher matrix technique to compute quadratic band power estimates. This allows an exact calculation of window functions, including the integral constraint, in addition to the production of a power spectrum with uncorrelated error bars. Our results with this larger data set agree well with previous studies. We analyze 101Mpc/h and 130Mpc/h volume-limited subsets in addition to the full magnitude-limited sample, and our results are well fit by, e.g., Lambda-CDM models with bias b=1.2, 1.4 and 1.4, respectively. We estimate the effect of extinction using the Schlegel, Finkbeiner & Davis dust map. Our results are exclusively for the redshift space galaxy power spectrum, so they can only be compared with theoretical predictions if appropriate corrections are made for biasing and redshift space distortions.

The Muenster Redshift Project. II. The Redshift Space Galaxy Power Spectrum

The redshift space galaxy power spectrum is estimated using magnitude-limited samples of up to 87,558 galaxies with redshifts z ≤ 0.2 and magnitudes rF ≤ 18.0 mag. Although the random redshift errors are comparatively large (σz = 0.031), the present survey sample gives reliable power spectral densities for wavenumbers 0.0125 ≤ k ≤ 0.15 h Mpc–1 corresponding to wavelengths 40 ≤ λ ≤ 500 h–1 Mpc. The Muenster Redshift Project data give a clear indication for the existence of a turnover in the shape of the power spectrum near wavelengths of 160 h–1 Mpc.