Observed galaxy clustering exhibits local transverse statistical isotropy around the line of sight (LOS). The variation of the LOS across a galaxy survey complicates the measurement of the observed ...clustering as a function of the angle to the LOS, as fast Fourier transforms (FFTs) based on Cartesian grids, cannot individually allow for this. Recent advances in methodology for calculating LOS-dependent clustering in Fourier space include the realization that power spectrum LOS-dependent moments can be constructed from sums over galaxies, based on approximating the LOS to each pair of galaxies by the LOS to one of them. We show that we can implement this method using multiple FFTs, each measuring the LOS-weighted clustering along different axes. The Nlog N nature of FFTs means that the computational speed-up is a factor of >1000 compared with summing over galaxies. This development should be beneficial for future projects such as DESI and Euclid which will provide an order of magnitude more galaxies than current surveys.
ABSTRACT
We present an improved framework for estimating the growth rate of large-scale structure, using measurements of the galaxy–velocity cross-correlation in configuration space. We consider ...standard estimators of the velocity autocorrelation function, ψ1 and ψ2, the two-point galaxy correlation function, ξgg, and introduce a new estimator of the galaxy–velocity cross-correlation function, ψ3. By including pair counts measured from random catalogues of velocities and positions sampled from distributions characteristic of the true data, we find that the variance in the galaxy–velocity cross-correlation function is significantly reduced. Applying a covariance analysis and χ2 minimization procedure to these statistics, we determine estimates and errors for the normalized growth rate fσ8 and the parameter β = f/b, where b is the galaxy bias factor. We test this framework on mock hemisphere data sets for redshift z < 0.1 with realistic velocity noise constructed from the l-picola simulation code, and find that we are able to recover the fiducial value of fσ8 from the joint combination of ψ1 + ψ2 + ψ3 + ξgg, with 15 per cent accuracy from individual mocks. We also recover the fiducial fσ8 to within 1σ regardless of the combination of correlation statistics used. When we consider all four statistics together we find that the statistical uncertainty in our measurement of the growth rate is reduced by $59{{\ \rm per\ cent}}$ compared to the same analysis only considering ψ2, by $53{{\ \rm per\ cent}}$ compared to the same analysis only considering ψ1, and by $52{{\ \rm per\ cent}}$ compared to the same analysis jointly considering ψ1 and ψ2.
We measure the growth rate and its evolution using the anisotropic clustering of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 (DR14) quasar sample, which includes ...|$148\, 659$| quasars covering the wide redshift range of 0.8 < z < 2.2 and a sky area of |$2112.90\, \rm deg^2$|. To optimize measurements we deploy a redshift-dependent weighting scheme, which allows us to avoid binning and perform the data analysis consistently including the redshift evolution across the sample. We perform the analysis in Fourier space, and use the redshift evolving power spectrum multipoles to measure the redshift-space distortion parameter fσ_8 and parameters controlling the anisotropic projection of the cosmological perturbations. We measure fσ_8(z = 1.52) = 0.43 ± 0.05 and dfσ_8/dz(z = 1.52) = −0.16 ± 0.08, consistent with the expectation for a lambda cold dark matter cosmology as constrained by the Planck experiment.
ABSTRACT
Baryon acoustic oscillations (BAOs) represent one of the cleanest probes of dark energy, allowing for tests of the cosmological model through the measurement of distance and expansion rate ...from a 3D galaxy distribution. The signal appears at large scales in the correlation function where linear theory applies, allowing for the construction of accurate models. However, due to the lower number of modes available at these scales, sample variance has a significant impact on the signal, and may sharpen or widen the underlying peak. Therefore, equivalent mock realizations of a galaxy survey present different errors in the position of the peak when uncertainties are estimated from the posterior probability distribution corresponding to the individual mocks. Hence, the posterior width, often quoted as the error in BAO survey measurements, is subject to sample noise. A different definition of the error is provided by the asymptotic variance of the maximum likelihood estimator, which involves the average over multiple realizations, and is not subject to sample noise. In this work, we reanalyse the main galaxy survey data available for BAO measurements and quantify the impact of the noise component on the error quoted for BAO measurements. We quantify the difference between three definitions of the error: the confidence region computed from a single posterior, the average of the variances of many realizations, and the Fisher matrix prediction assuming a Gaussian likelihood. We also explore the impact of a ‘detectability prior’ based on the significance of the BAO detection.
ABSTRACT
Combining different observational probes, such as galaxy clustering and weak lensing, is a promising technique for unveiling the physics of the Universe with upcoming dark energy ...experiments. Whilst this strategy significantly improves parameter constraints, decreasing the degeneracies of individual analyses and controlling the systematics, processing data from tens of millions of galaxies is not a trivial task. In this work, we derive and test a new compressed statistic for joint clustering and lensing data analysis, maximizing the scientific return and decreasing the computational cost. Our approach compresses the data by up-weighting the components most sensitive to the parameters of interest, with no loss of information, taking into account information from the cross-correlation between the two probes. We derive optimal redshift weights which may be applied to individual galaxies when testing a given statistic and cosmological model.
ABSTRACT
Galaxy peculiar velocities provide an integral source of cosmological information that can be harnessed to measure the growth rate of large-scale structure and constrain possible extensions ...to General Relativity. In this work, we present a method for extracting the information contained within galaxy peculiar velocities through an ensemble of direct peculiar velocity and galaxy clustering correlation statistics, including the effects of redshift space distortions, using data from the 6-degree Field Galaxy Survey. Our method compares the auto- and cross-correlation function multipoles of these observables, with respect to the local line of sight, with the predictions of cosmological models. We find that the uncertainty in our measurement is improved when combining these two sources of information in comparison to fitting to either peculiar velocity or clustering information separately. When combining velocity and density statistics in the range $27 \lt s \lt 123 \, h^{-1}$ Mpc we obtain a value for the local growth rate of fσ8 = 0.358 ± 0.075 and for the linear redshift distortion parameter β = 0.298 ± 0.065, recovering both with 20.9 per cent and 21.8 per cent accuracy, respectively. We conclude this work by comparing our measurement with other recent local measurements of the growth rate, spanning different data sets and methodologies. We find that our results are in broad agreement with those in the literature and are fully consistent with ΛCDM cosmology. Our methods can be readily scaled to analyse upcoming large galaxy surveys and achieve accurate tests of the cosmological model.
Abstract
Galaxy clustering data from current and upcoming large-scale structure surveys can provide strong constraints on primordial non-Gaussianity through the scale-dependent halo bias. To fully ...exploit the information from galaxy surveys, optimal analysis methods need to be developed and applied to the data. Since the halo bias is sensitive to local non-Gaussianity predominately at large scales, the volume of a given survey is crucial. Consequently, for such analyses we do not want to split into redshift bins, which would lead to information loss due to edge effects, but instead analyse the full sample. We present an optimal technique to directly constrain local non-Gaussianity parametrized by $f_\mathrm{NL}^\mathrm{loc}$, from galaxy clustering by applying redshift weights to the galaxies. We derive a set of weights to optimally measure the amplitude of local non-Gaussianity, $f_\mathrm{NL}^\mathrm{loc}$, discuss the redshift weighted power spectrum estimators, outline the implementation procedure and test our weighting scheme against lognormal catalogues for two different surveys: the quasar sample of the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) and the emission line galaxy sample of the Dark Energy Spectroscopic Instrument (DESI) survey. We find an improvement of 30 per cent for eBOSS and 6 per cent for DESI compared to the standard Feldman, Kaiser, and Peacock weights, although these predictions are sensitive to the bias model assumed.
ABSTRACT
The theoretical basis of dark energy remains unknown and could signify a need to modify the laws of gravity on cosmological scales. In this study, we investigate how the clustering and ...motions of galaxies can be used as probes of modified gravity theories, using galaxy and direct peculiar velocity auto- and cross-correlation functions. We measure and fit these correlation functions in simulations of ΛCDM, DGP, and f(R) cosmologies and, by extracting the characteristic parameters of each model, we show that these theories can be distinguished from General Relativity (GR) using these measurements. We present forecasts showing that with sufficiently large data samples, this analysis technique is a competitive probe that can help place limits on allowed deviations from GR. For example, a peculiar velocity survey reaching to z = 0.5 with $20{{\ \rm per\ cent}}$ distance accuracy would constrain model parameters to 3-σ confidence limits log10|fR0| < −6.45 for f(R) gravity and $r_\mathrm{ c} \gt 2.88 \, \mathrm{ c}/H_0$ for nDGP, assuming a fiducial GR model.
We develop a new method, which is based on the optimal redshift weighting scheme, to extract the maximal tomographic information of baryonic acoustic oscillations (BAO) and redshift space distortions ...(RSD) from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 quasar (DR14Q) survey. We validate our method using the Extended Zel’dovich mocks, and apply our pipeline to the eBOSS DR14Q sample in the redshift range of 0.8 < |$z$| < 2.2. We report a joint measurement of fσ_8 and two-dimensional BAO parameters D_A and H at four effective redshifts of |$z$|_eff = 0.98, 1.23, 1.52, and 1.94, and provide the full data covariance matrix. Using our measurement combined with BOSS DR12, Main Galaxy Sample (MGS), and 6 degree Field Galaxy Survey (6dFGS) BAO measurements, we find that the existence of dark energy is supported by observations at a 7.4σ significance level. Combining our measurement with BOSS DR12 and Planck observations, we constrain the gravitational growth index to be γ = 0.580 ± 0.082, which is fully consistent with the prediction of general relativity. This paper is part of a set that analyses the eBOSS DR14 quasar sample.
We analyse the clustering of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample (DR14Q). We measure the redshift space distortions using ...the power-spectrum monopole, quadrupole, and hexadecapole inferred from 148 659 quasars between redshifts 0.8 and 2.2, covering a total sky footprint of 2112.9 deg^2. We constrain the logarithmic growth of structure times the amplitude of dark matter density fluctuations, fσ_8, and the Alcock–Paczynski dilation scales that allow constraints to be placed on the angular diameter distance (z) and the Hubble H(z) parameter. At the effective redshift of z_eff = 1.52, fσ_8(z_eff) = 0.420 ± 0.076, $$H(z_{\rm eff})=162\pm 12\, (r_s^{\rm fid}/r_s)\,{\rm km\, s}^{-1}\,{\rm Mpc}^{-1}$$, and $$D_A(z_{\rm eff})=1.85\pm 0.11\times 10^3\,(r_s/r_s^{\rm fid})\,{\rm Mpc}$$, where r_s is the comoving sound horizon at the baryon drag epoch and the superscript ‘fid’ stands for its fiducial value. The errors take into account the full error budget, including systematics and statistical contributions. These results are in full agreement with the current Λ-Cold Dark Matter cosmological model inferred from Planck measurements. Finally, we compare our measurements with other eBOSS companion papers and find excellent agreement, demonstrating the consistency and complementarity of the different methods used for analysing the data.
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