Baryon Acoustic Scale Research Articles

Observational constraints on scale-dependent cosmology

This paper examines a cosmological model of scale-dependent gravity. The gravitational action is taken to be the Einstein–Hilbert term supplemented with a cosmological constant, where the couplings, Gk and Λk, run with the energy scale k. Also, notice that, by construction, our formalism recovers general relativity when in the limit of constant Newton’s coupling. Two sub-models based on the scale-dependent cosmological model are confronted with recent observational data from: (i) the Hubble parameter H(z), (ii) distance modulus μ(z), and (iii) baryon acoustic scale evolution as functions of redshift (BAO). The viability of the model is discussed, obtaining the best-fit parameters and the maximum likelihood contours for these observables. Finally, a joint analysis is performed for H(z)+μ(z)＋BAO.

Baryon acoustic scale at zeff = 0.166 with the SDSS blue galaxies

ABSTRACT The baryon acoustic oscillations (BAOs) phenomenon provides a unique opportunity to establish a standard ruler at any epoch in the history of the evolving universe. The key lies in identifying a suitable cosmological tracer to conduct the measurement. In this study, we focus on quantifying the sound horizon scale of BAO in the Local Universe. Our chosen cosmological tracer is a sample of blue galaxies from the Sloan Digital Sky Survey (SDSS), positioned at the effective redshift $z_{{\rm eff}} = 0.166$. Utilizing Planck-CMB input values for redshift-to-distance conversion, we derive the BAO scale $s_{{\rm BAO}} = 100.28 ^{+10.79} _{-22.96}$ Mpc h−1 at the 1$\sigma$ confidence level. Subsequently, we extrapolate the BAO signal scale in redshift space: $\Delta z_{{\rm BAO}}(z_{\rm eff}=0.166)=0.0361^{+0.00262}_ {-0.0055}$. This measurement holds the potential to discriminate among dark energy models within the Local Universe. To validate the robustness of our methodology for BAO scale measurement, we conduct three additional BAO analyses using different cosmographic approaches for distance calculation from redshifts. These tests aim to identify possible biases or systematics in our measurements of $s_{{\rm BAO}}$. Encouragingly, our diverse cosmographic approaches yield results in statistical agreement with the primary measurement, indicating no significant deviations. Conclusively, our study contributes with a novel determination of the BAO scale in the Local Universe, at $z_{{\rm eff}} = 0.166$, achieved through the analysis of the SDSS blue galaxies cosmic tracer.

Euclid: Constraining ensemble photometric redshift distributions with stacked spectroscopy

Context. The ESA Euclid mission will produce photometric galaxy samples over 15 000 square degrees of the sky that will be rich for clustering and weak lensing statistics. The accuracy of the cosmological constraints derived from these measurements will depend on the knowledge of the underlying redshift distributions based on photometric redshift calibrations. Aims. A new approach is proposed to use the stacked spectra from Euclid slitless spectroscopy to augment broad-band photometric information to constrain the redshift distribution with spectral energy distribution fitting. The high spectral resolution available in the stacked spectra complements the photometry and helps to break the colour-redshift degeneracy and constrain the redshift distribution of galaxy samples. Methods. We modelled the stacked spectra as a linear mixture of spectral templates. The mixture may be inverted to infer the underlying redshift distribution using constrained regression algorithms. We demonstrate the method on simulated Vera C. Rubin Observatory and Euclid mock survey data sets based on the Euclid Flagship mock galaxy catalogue. We assess the accuracy of the reconstruction by considering the inference of the baryon acoustic scale from angular two-point correlation function measurements. Results. We selected mock photometric galaxy samples at redshift z > 1 using the self-organising map algorithm. Considering the idealised case without dust attenuation, we find that the redshift distributions of these samples can be recovered with 0.5% accuracy on the baryon acoustic scale. The estimates are not significantly degraded by the spectroscopic measurement noise due to the large sample size. However, the error degrades to 2% when the dust attenuation model is left free. We find that the colour degeneracies introduced by attenuation limit the accuracy considering the wavelength coverage of Euclid near-infrared spectroscopy.

Geometry versus growth

We carry out a multi-probe self-consistency test of the flat Lambda Cold Dark Matter (ΛCDM) model with the aim of exploring potential causes of the reported tensions between high- and low-redshift cosmological observations. We divide the model into two theory regimes determined by the smooth background (geometry) and the evolution of matter density fluctuations (growth), each governed by an independent set of ΛCDM cosmological parameters. This extended model is constrained by a combination of weak gravitational lensing measurements from the Kilo-Degree Survey, galaxy clustering signatures extracted from Sloan Digital Sky Survey campaigns and the Six-Degree Field Galaxy Survey, and the angular baryon acoustic scale and the primordial scalar fluctuation power spectrum measured in Planck cosmic microwave background (CMB) data. For both the weak lensing data set individually and the combined probes, we find strong consistency between the geometry and growth parameters, as well as with the posterior of standard ΛCDM analysis. In the non-split analysis, for which one single set of parameters was used, tension in the amplitude of matter density fluctuations as measured by the parameter S8 persists at around 3σ, with a 1.5% constraint of S8 = 0.776−0.008+0.016 for the combined probes. We also observe a less significant preference (at least 2σ) for higher values of the Hubble constant, H0 = 70.5−1.5+0.7 km s−1 Mpc−1, as well as for lower values of the total matter density parameter Ωm = 0.289−0.005+0.007 compared to the full Planck analysis. Including the subset of the CMB information in the probe combination enhances these differences rather than alleviate them, which we link to the discrepancy between low and high multipoles in Planck data. Our geometry versus growth analysis does not yet yield clear signs regarding whether the origin of the discrepancies lies in ΛCDM structure growth or expansion history but holds promise as an insightful test for forthcoming, more powerful data.

Does jackknife scale really matter for accurate large-scale structure covariances?

ABSTRACT The jackknife method gives an internal covariance estimate for large-scale structure surveys and allows model-independent errors on cosmological parameters. Using the SDSS-III BOSS CMASS sample, we study how the jackknife size and number of resamplings impact the precision of the covariance estimate on the correlation function multipoles and the error on the inferred baryon acoustic scale. We compare the measurement with the MultiDark Patchy mock galaxy catalogues, and we also validate it against a set of lognormal mocks with the same survey geometry. We build several jackknife configurations that vary in size and number of resamplings. We introduce the Hartlap factor in the covariance estimate that depends on the number of jackknife resamplings. We also find that it is useful to apply the tapering scheme to estimate the precision matrix from a limited number of resamplings. The results from CMASS and mock catalogues show that the error estimate of the baryon acoustic scale does not depend on the jackknife scale. For the shift parameter α, we find an average error of 1.6 per cent, 2.2 per cent and 1.2 per cent, respectively, from CMASS, Patchy, and lognormal jackknife covariances. Despite these uncertainties fluctuate significantly due to some structural limitations of the jackknife method, our α estimates are in reasonable agreement with published pre-reconstruction analyses. Jackknife methods will provide valuable and complementary covariance estimates for future large-scale structure surveys.

Two-point Statistics without Bins: A Continuous-function Generalization of the Correlation Function Estimator for Large-scale Structure

Abstract The two-point correlation function (2pcf) is the key statistic in structure formation; it measures the clustering of galaxies or other density field tracers. Estimators of the 2pcf, including the standard Landy–Szalay (LS) estimator, evaluate the 2pcf in hard-edged separation bins, which is scientifically inappropriate and results in a poor trade-off between bias and variance. We present a new 2pcf estimator, the Continuous-Function Estimator, which generalizes LS to a continuous representation and obviates binning in separation or any other pair property. Our estimator, inspired by the mathematics of least-squares fitting, replaces binned pair counts with projections onto basis functions; it outputs the best linear combination of basis functions to describe the 2pcf. The choice of basis can take into account the expected form of the 2pcf, as well as its dependence on pair properties other than separation. We show that the Continuous-Function Estimator with a cubic-spline basis better represents the shape of the 2pcf compared to LS. We also estimate directly the baryon acoustic scale, using a small number of physically motivated basis functions. Critically, this leads to a reduction in the number of mock catalogs required for covariance estimation, which is currently the limiting step in many 2pcf analyses. We discuss further applications of the Continuous-Function Estimator, including determination of the dependence of clustering on galaxy properties and searches for potential inhomogeneities or anisotropies in large-scale structure.

Constraints on decaying dark matter from weak lensing and cluster counts

We revisit a cosmological constraint on dark matter decaying into dark radiation at late times. In Enqvist et al. (2015), we mainly focused on the effects of decaying dark matter (DDM) on the cosmic microwave background (CMB) and nonlinear matter power spectrum. Extending our previous analysis, here we use N-body simulation to investigate how DDM affects the halo mass function. This allows us to incorporate the cluster counts observed by the Sunyaev-Zel'dovich effect to study a bound on the lifetime of DDM . We also update the data of CMB and cosmic shear power spectrum with the Planck 2015 results and KiDS450 observations, respectively. From these cosmological observations, we obtain an lower bound on the lifetime Γ−1⩾ 154 Gyr from the Planck2015 results (CMB+SZ cluster count) combined with the KiDS450 and the recent measurements of the baryon acoustic scale.

The transverse baryonic acoustic scale from the SDSS DR11 galaxies

We report five measurements of the transverse baryonic acoustic scale, θBAO, obtained from the angular two-point correlation function calculation for Luminous Red Galaxies of the eleventh data release of the Sloan Digital Sky Survey (SDSS). Each measurement has been obtained by considering a thin redshift shell (Δz=0.01 and 0.02) in the interval z ∈ [0.565, 0.660], which contains a large density of galaxies ( ~ 20, 000 galaxies/redshift shell). Differently from the three-dimensional Baryon Acoustic Oscillations (BAO) measurements, these data points are obtained almost model-independently and provide a Cosmic Microwave Background (CMB)-independent way to estimate the sound horizon rs. Assuming a time-dependent equation-of-state parameter for the dark energy, we also discuss constraints on the main cosmological parameters from θBAO and CMB data.

Accuracy of cosmological parameters using the baryon acoustic scale

Percent-level measurements of the comoving baryon acoustic scale standard ruler can be used to break degeneracies in parameter constraints from the CMB alone. The sound horizon at the epoch of baryon drag is often used as a proxy for the scale of the peak in the matter density correlation function, and can conveniently be calculated quickly for different cosmological models. However, the measurements are not directly constraining this scale, but rather a measurement of the full correlation function, which depends on the detailed evolution through decoupling. We assess the level of reliability of parameter constraints based on a simple approximation of the acoustic scale compared to a more direct determination from the full numerical two-point correlation function. Using a five-parameter fitting technique similar to recent BAO data analyses, we find that for standard ΛCDM models and extensions with massive neutrinos and additional relativistic degrees of freedom, the approximation is at better than 0.15% for most parameter combinations varying over reasonable ranges.

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: galaxy clustering measurements in the low-redshift sample of Data Release 11

We present the distance measurement to z = 0.32 using the 11th data release of the Sloan Digital Sky Survey-III Baryon Acoustic Oscillation Survey (BOSS). We use 313,780 galaxies of the low-redshift (LOWZ) sample over 7,341 square-degrees to compute $D_V = (1264 \pm 25)(r_d/r_{d,fid})$ - a sub 2% measurement - using the baryon acoustic feature measured in the galaxy two-point correlation function and power-spectrum. We compare our results to those obtained in DR10. We study observational systematics in the LOWZ sample and quantify potential effects due to photometric offsets between the northern and southern Galactic caps. We find the sample to be robust to all systematic effects found to impact on the targeting of higher-redshift BOSS galaxies, and that the observed north-south tensions can be explained by either limitations in photometric calibration or by sample variance, and have no impact on our final result. Our measurement, combined with the baryonic acoustic scale at z = 0.57, is used in Anderson et al. (2013a) to constrain cosmological parameters.

Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields

Models of galaxy and halo clustering commonly assume that the tracers can be treated as a continuous field locally biased with respect to the underlying mass distribution. In the peak model pioneered by Bardeen et al. [Astrophys. J. 304, 15 (1986)], one considers instead density maxima of the initial, Gaussian mass density field as an approximation to the formation site of virialized objects. In this paper, the peak model is extended in two ways to improve its predictive accuracy. First, we derive the two-point correlation function of initial density peaks up to second order and demonstrate that a peak-background split approach can be applied to obtain the $k$-independent and $k$-dependent peak bias factors at all orders. Second, we explore the gravitational evolution of the peak correlation function within the Zel'dovich approximation. We show that the local (Lagrangian) bias approach emerges as a special case of the peak model, in which all bias parameters are scale independent and there is no statistical velocity bias. We apply our formulas to study how the Lagrangian peak biasing, the diffusion due to large scale flows, and the mode coupling due to nonlocal interactions affect the scale dependence of bias from small separations up to the baryon acoustic oscillation (BAO) scale. For $2\ensuremath{\sigma}$ density peaks collapsing at $z=0.3$, our model predicts a $\ensuremath{\sim}5%$ residual scale-dependent bias around the acoustic scale that arises mostly from first order Lagrangian peak biasing (as opposed to second order gravity mode coupling). We also search for a scale dependence of bias in the large scale autocorrelation of massive halos extracted from a very large $N$-body simulation provided by the MICE Collaboration. For halos with mass $M\ensuremath{\gtrsim}{10}^{14}{\mathrm{M}}_{\ensuremath{\bigodot}}/h$, our measurements demonstrate a scale-dependent bias across the BAO feature which is very well reproduced by a prediction based on the peak model.

First Cosmological Constraints on Dark Energy from the Radial Baryon Acoustic Scale

We present cosmological constraints arising from the first measurement of the radial (line-of-sight) baryon acoustic oscillations (BAO) scale in the large scale structure traced by the galaxy distribution. Here we use these radial BAO measurements at z = 0.24 and z = 0.43 to derive new constraints on dark energy and its equation of state for a flat universe, without any other assumptions on the cosmological model: w = -1.14 + or - 0.39 (assumed constant), Omega(m) = 0.24(-0.05);(+0.06). If we drop the assumption of flatness and include previous cosmic microwave background and supernova data, we find w = -0.974 + or - 0.058, Omega(m) = 0.271 + or - 0.015, and Omega(k) = -0.002 + or - 0.006, in good agreement with a flat cold dark matter cosmology with a cosmological constant. To our knowledge, these are the most stringent constraints on these parameters to date under our stated assumptions.

Can We Avoid Dark Energy?

The idea that we live near the center of a large, nonlinear void has attracted attention recently as an alternative to dark energy or modified gravity. We show that an appropriate void profile can fit both the latest cosmic microwave background and supernova data. However, this requires either a fine-tuned primordial spectrum or a Hubble rate so low as to rule these models out. We also show that measurements of the radial baryon acoustic scale can provide very strong constraints. Our results present a serious challenge to void models of acceleration.

Resumming cosmological perturbations via the Lagrangian picture: One-loop results in real space and in redshift space

We develop a new approach to study the nonlinear evolution in the large-scale structure of the Universe both in real space and in redshift space, extending the standard perturbation theory of gravitational instability. Infinite series of terms in standard Eulerian perturbation theory are resummed as a result of our starting from a Lagrangian description of perturbations. Delicate nonlinear effects on scales of the baryon acoustic oscillations are more accurately described by our method than the standard one. Our approach differs from other resummation techniques recently proposed, such as the renormalized perturbation theory, etc., in that we use simple techniques and thus resulting equations are undemanding to evaluate, and in that our approach is capable of quantifying the nonlinear effects in redshift space. The power spectrum and correlation function of our approach are in good agreement with numerical simulations in literature on scales of baryon acoustic oscillations. Especially, nonlinear effects on the baryon acoustic peak of the correlation function are accurately described both in real space and in redshift space. Our approach provides a unique opportunity to analytically investigate the nonlinear effects on baryon acoustic scales in observable redshift space, which is requisite in constraining the nature of dark energy, the curvature of the Universe, etc., by redshift surveys.

Lensing corrections to features in the angular two-point correlation function and power spectrum

It is well known that magnification bias, the modulation of galaxy or quasar source counts by gravitational lensing, can change the observed angular correlation function. We investigate magnification-induced changes to the shape of the observed correlation function $w(\ensuremath{\theta})$, and the angular power spectrum ${C}_{\ensuremath{\ell}}$, paying special attention to the matter-radiation equality peak and the baryon wiggles. Lensing effectively mixes the correlation function of the source galaxies with that of the matter correlation at the lower redshifts of the lenses distorting the observed correlation function. We quantify how the lensing corrections depend on the width of the selection function, the galaxy bias $b$, and the number count slope $s$. The lensing correction increases with redshift and larger corrections are present for sources with steep number count slopes and/or broad redshift distributions. The most drastic changes to ${C}_{\ensuremath{\ell}}$ occur for measurements at high redshifts ($z\ensuremath{\gtrsim}1.5$) and low multipole moment ($\ensuremath{\ell}\ensuremath{\lesssim}100$). For the source distributions we consider, magnification bias can shift the location of the matter-radiation equality scale by 1%--6% at $z\ensuremath{\sim}1.5$ and by $z\ensuremath{\sim}3.5$ the shift can be as large as 30%. The baryon bump in ${\ensuremath{\theta}}^{2}w(\ensuremath{\theta})$ is shifted by $\ensuremath{\lesssim}1%$ and the width is typically increased by $\ensuremath{\sim}10%$. Shifts of $\ensuremath{\gtrsim}0.5%$ and broadening $\ensuremath{\gtrsim}20%$ occur only for very broad selection functions and/or galaxies with $(5s\ensuremath{-}2)/b\text{ }\ensuremath{\gtrsim}\text{ }2$. However, near the baryon bump the magnification correction is not constant but is a gently varying function which depends on the source population. Depending on how the $w(\ensuremath{\theta})$ data is fitted, this correction may need to be accounted for when using the baryon acoustic scale for precision cosmology.