Baryon Acoustic Oscillation Peak Position Research Articles

Mixing bispectrum multipoles under geometric distortions

ABSTRACT We derive general expressions for how the Alcock–Paczynski distortions affect the power spectrum and the bispectrum of cosmological fields. We compute explicit formulas for the mixing coefficients of bispectrum multipoles in the linear approximation. The leading-order effect for the bispectrum is the uniform dilation of all three wavevectors. The mixing coefficients depend on the shape of the bispectrum triplet. Our results for the bispectrum multipoles are framed in terms of the ‘natural’ basis of the lengths of three wavevectors but can be easily generalized for other bases and reduction schemes. Our validation tests confirm that the linear approximation is extremely accurate for all power spectrum multipoles. The linear approximation is accurate for the bispectrum monopole but results in sub-per cent level inaccuracies for the bispectrum quadrupole and fails for the bispectrum hexadecapole. Our results can be used to simplify the analysis of the bispectrum from galaxy surveys, especially the measurement of the baryon acoustic oscillation peak position. They can be used to replace numeric schemes with exact analytical formulae.

Model selection using baryon acoustic oscillations in the final SDSS-IV release

The baryon acoustic oscillation (BAO) peak, seen in the cosmic matter distribution at redshifts up to [Formula: see text]3.5, reflects the continued expansion of the sonic horizon first identified in temperature anisotropies of the cosmic microwave background. The BAO peak position can now be measured to better than [Formula: see text]1% accuracy using galaxies and [Formula: see text]1.4–1.6% precision with Ly-[Formula: see text] forests and the clustering of quasars. In conjunction with the Alcock–Paczyński (AP) effect, which arises from the changing ratio of angular to spatial/redshift size of (presumed) spherically-symmetric source distributions with distance, the BAO measurement is viewed as one of the most powerful tools to use in assessing the geometry of the Universe. In this paper, we employ five BAO peak measurements from the final release of the Sloan Digital Sky Survey IV, at average redshifts [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], to carry out a direct head-to-head comparison of the standard model, [Formula: see text]CDM, and one of its principal competitors, known as the [Formula: see text] universe. For completeness, we complement the AP diagnostic with a volume-averaged distance probe that assumes a constant comoving distance scale [Formula: see text]. Both probes are free of uncertain parameters, such as the Hubble constant, and are therefore ideally suited for this kind of model selection. We find that [Formula: see text] is favored by these measurements over the standard model based solely on the AP effect, with a likelihood [Formula: see text]75% versus [Formula: see text]25%, while Planck-[Formula: see text]CDM is favored over [Formula: see text] based solely on the volume-averaged distance probe, with a likelihood [Formula: see text] versus [Formula: see text]20%. A joint analysis using both probes produces an inconclusive outcome, yielding comparable likelihoods to both models. We are therefore not able to confirm with this work that the BAO data, on their own, support an accelerating Universe.

Line confusion in spectroscopic surveys and its possible effects: shifts in Baryon Acoustic Oscillations position

ABSTRACT Roman Space Telescope will survey about 17 million emission-line galaxies over a range of redshifts. Its main targets are Hα emission-line galaxies at low redshifts (z < 2) and [O iii] emission-line galaxies at high redshifts (z > 2). The Roman Space Telescope will estimate the redshift of these galaxies with single-line identification. This suggests that other emission-line galaxies may be misidentified as the main targets. In particular, it is hard to distinguish between the H β and [O iii] lines as the two lines are close in wavelength and hence the photometric information may not be sufficient to separate them reliably. Misidentifying H β emitter as [O iii] emitter will cause a shift in the inferred radial position of the galaxy by approximately 90 Mpc h−1. This length-scale is similar to the Baryon Acoustic Oscillation (BAO) scale and could shift and broaden the BAO peak, possibly introduce errors in determining the BAO peak position. We qualitatively describe the effect of this new systematic and further quantify it with a light-cone simulation with emission-line galaxies. Our results show a systematic shift in the recovered isotropic BAO positions that depends on the percentage of interlopers (percentage of ${\rm H}\,\beta$) in the sample. The systematic shift can be as large as $0.1{-}0.3\,\mathrm{ per}\,\mathrm{ cent} \, {\rm x}\, {{\%}}{\rm H}\,\beta$ for analysis performed at redshifts z = 1.3−1.9.

Measuring the baryon acoustic oscillation peak position with different galaxy selections

ABSTRACT We investigate if, for a fixed number density of targets and redshift, there is an optimal way to select a galaxy sample in order to measure the baryon acoustic oscillation (BAO) scale, which is used as a standard ruler to constrain the cosmic expansion. Using the mock galaxy catalogue built by Smith et al. in the Millennium-XXL N-body simulation with a technique to assign galaxies to dark matter haloes based on halo occupation distribution modelling, we consider the clustering of galaxies selected by luminosity, colour and local density. We assess how well the BAO scale can be extracted by fitting a template to the power spectrum measured for each sample. We find that the BAO peak position is recovered equally well for samples defined by luminosity or colour, while there is a bias in the BAO scale recovered for samples defined by density. The BAO position is contracted to smaller scales for the densest galaxy quartile and expanded to large scales for the two least dense galaxy quartiles. For fixed galaxy number density, density-selected samples have higher uncertainties in the recovered BAO scale than luminosity- or colour-selected samples.

Improving baryon acoustic oscillation measurement with the combination of cosmic voids and galaxies

ABSTRACT We develop a methodology to optimize the measurement of baryon acoustic oscillation (BAO) from a given galaxy sample. In our previous work, we demonstrated that one can measure BAO from tracers in underdense regions (voids). In this study, we combine the overdense and underdense tracers (galaxies and voids) to obtain better constraints on the BAO scale. To this end, we modify the de-wiggled BAO model with an additional parameter to describe both the BAO peak and the underlying exclusion pattern of void 2PCFs. We show that after applying BAO reconstruction to galaxies, the BAO peak scale of both galaxies and voids are unbiased using the modified model. Furthermore, we use a new 2PCF estimator for a multitracer analysis with galaxies and voids. In simulations, the joint sample improves by about 10 per cent the constraint for the post-reconstruction BAO peak position compared to the result from galaxies alone, which is equivalent to an enlargement of the survey volume by 20 per cent. Applying this method to the BOSS DR12 data, we have an 18 per cent improvement for the low-z sample (0.2 < z < 0.5), but a worse constraint for the high-z sample (0.5 < z < 0.75), which is consistent with statistical fluctuations for the current survey volume. Future larger samples will give more robust improvements due to less statistical fluctuations.

Baryon acoustic oscillations from the cross-correlation of Lyαabsorption and quasars in eBOSS DR14

We present a measurement of the baryon acoustic oscillation (BAO) scale at redshiftz = 2.35 from the three-dimensional correlation of Lyman-α(Lyα) forest absorption and quasars. The study uses 266 590 quasars in the redshift range 1.77 < z < 3.5 from the Sloan Digital Sky Survey (SDSS) Data Release 14 (DR14). The sample includes the first two years of observations by the SDSS-IV extended Baryon Oscillation Spectroscopic Survey (eBOSS), providing new quasars and re-observations of BOSS quasars for improved statistical precision. Statistics are further improved by including Lyαabsorption occurring in the Lyβwavelength band of the spectra. From the measured BAO peak position along and across the line of sight, we determined the Hubble distanceDHand the comoving angular diameter distanceDMrelative to the sound horizon at the drag epochrd:DH(z = 2.35)/rd = 9.20 ± 0.36 andDM(z = 2.35)/rd = 36.3 ± 1.8. These results are consistent at 1.5σwith the prediction of the best-fit spatially-flat cosmological model with the cosmological constant reported for thePlanck(2016) analysis of cosmic microwave background anisotropies. Combined with the Lyαauto-correlation measurement presented in a companion paper, the BAO measurements atz = 2.34 are within 1.7σof the predictions of this model.

Baryon acoustic oscillations from the complete SDSS-III Lyα-quasar cross-correlation function at z = 2.4

We present a measurement of baryon acoustic oscillations (BAO) in the cross-correlation of quasars with the Lyα-forest flux transmission at a mean redshift ofz= 2.40. The measurement uses the complete Sloan Digital Sky Survey (SDSS-III) data sample: 168 889 forests and 234 367 quasars from the SDSS data release DR12. In addition to the statistical improvement on our previous study using DR11, we have implemented numerous improvements at the analysis level enabling a more accurate measurement of this cross-correlation. We have also developed the first simulations of the cross-correlation that allow us to test different aspects of our data analysis and to search for potential systematic errors in the determination of the BAO peak position. We measure the two ratiosDH(z= 2.40) /rd= 9.01 ± 0.36 andDM(z= 2.40) /rd= 35.7 ± 1.7, where the errors include marginalization over the non-linear velocity of quasars and the cross-correlation of metals and quasars, among other effects. These results are within 1.8σof the prediction of the flat-ΛCDM model describing the observed cosmic microwave background anisotropies. We combine this study with the Lyα-forest auto-correlation function, yieldingDH(z= 2.40) /rd= 8.94 ± 0.22 andDM(z= 2.40) /rd= 36.6 ± 1.2, within 2.3σof the same flat-ΛCDM model.

Small-scale structure and the Lyman-α forest baryon acoustic oscillation feature

The baryon-acoustic oscillation (BAO) feature in the Lyman-$\alpha$ forest is one of the key probes of the cosmic expansion rate at redshifts z~2.5, well before dark energy is believed to have become dynamically significant. A key advantage of the BAO as a standard ruler is that it is a sharp feature and hence is more robust against broadband systematic effects than other cosmological probes. However, if the Lyman-$\alpha$ forest transmission is sensitive to the initial streaming velocity of the baryons relative to the dark matter, then the BAO peak position can be shifted. Here we investigate this sensitivity using a suite of hydrodynamic simulations of small regions of the intergalactic medium with a range of box sizes and physics assumptions; each simulation starts from initial conditions at the kinematic decoupling era (z~1059), undergoes a discrete change from neutral gas to ionized gas thermal evolution at reionization (z~8), and is finally processed into a Lyman-$\alpha$ forest transmitted flux cube. Streaming velocities suppress small-scale structure, leading to less violent relaxation after reionization. The changes in the gas distribution and temperature-density relation at low redshift are more subtle, due to the convergent temperature evolution in the ionized phase. The change in the BAO scale is estimated to be of the order of 0.12% at z=2.5; some of the major uncertainties and avenues for future improvement are discussed. The predicted streaming velocity shift would be a subdominant but not negligible effect (of order $0.26\sigma$) for the upcoming DESI Lyman-$\alpha$ forest survey, and exceeds the cosmic variance floor. It is hoped that this study will motivate additional theoretical work on the magnitude of the BAO shift, both in the Lyman-$\alpha$ forest and in other tracers of large-scale structure.

Baryon Acoustic Oscillations reconstruction with pixels

Gravitational non-linear evolution induces a shift in the position of the baryon acoustic oscillations (BAO) peak together with a damping and broadening of its shape that bias and degrades the accuracy with which the position of the peak can be determined. BAO reconstruction is a technique developed to undo part of the effect of non-linearities. We present and analyse a reconstruction method that consists of displacing pixels instead of galaxies and whose implementation is easier than the standard reconstruction method. We show that this method is equivalent to the standard reconstruction technique in the limit where the number of pixels becomes very large. This method is particularly useful in surveys where individual galaxies are not resolved, as in 21cm intensity mapping observations. We validate this method by reconstructing mock pixelated maps, that we build from the distribution of matter and halos in real- and redshift-space, from a large set of numerical simulations. We find that this method is able to decrease the uncertainty in the BAO peak position by 30-50% over the typical angular resolution scales of 21 cm intensity mapping experiments.

Measurement of baryon acoustic oscillation correlations atz = 2.3 with SDSS DR12 Lyα-Forests

We use flux-transmission correlations in \Lya forests to measure the imprint of baryon acoustic oscillations (BAO). The study uses spectra of 157,783 quasars in the redshift range $2.1\le z \le 3.5$ from the Sloan Digital Sky Survey (SDSS) Data Release 12 (DR12). Besides the statistical improvements on our previous studies using SDSS DR9 and DR11, we have implemented numerous improvements in the analysis procedure, allowing us to construct a physical model of the correlation function and to investigate potential systematic errors in the determination of the BAO peak position. The Hubble distance, $\DHub=c/H(z)$, relative to the sound horizon is $\DHub(z=2.33)/r_d=9.07 \pm 0.31$. The best-determined combination of comoving angular-diameter distance, $\DM$, and the Hubble distance is found to be $\DHub^{0.7}\DM^{0.3}/r_d=13.94\pm0.35$. This value is $1.028\pm0.026$ times the prediction of the flat-\lcdm model consistent with the cosmic microwave background (CMB) anisotropy spectrum. The errors include marginalization over the effects of unidentified high-density absorption systems and fluctuations in ultraviolet ionizing radiation. Independently of the CMB measurements, the combination of our results and other BAO observations determine the open-\lcdm density parameters to be $\om=0.296 \pm 0.029$, $\ol=0.699 \pm 0.100$ and $\Omega_k = -0.002 \pm 0.119$.

Large-scale analysis of the SDSS-III DR8 photometric luminous galaxies angular correlation function

We analyse the large-scale angular correlation function (ACF) of the CMASS luminous galaxies (LGs), a photometric-redshift catalogue based on the Data Release 8 (DR8) of the Sloan Digital Sky Survey-III. This catalogue contains over $600 \, \, 000$ LGs in the range $0.45 \leq z \leq 0.65$, which was split into four redshift shells of constant width. First, we estimate the constraints on the redshift-space distortion (RSD) parameters $b\sigma_8$ and $f\sigma_8$, where $b$ is the galaxy bias, $f$ the growth rate and $\sigma_8$ is the normalization of the perturbations, finding that they vary appreciably among different redshift shells, in agreement with previous results using DR7 data. When assuming constant RSD parameters over the survey redshift range, we obtain $f\sigma_8 = 0.69 \pm 0.21$, which agrees at the $1.5\sigma$ level with Baryon Oscillation Spectroscopic Survey DR9 spectroscopic results. Next, we performed two cosmological analyses, where relevant parameters not fitted were kept fixed at their fiducial values. In the first analysis, we extracted the baryon acoustic oscillation peak position for the four redshift shells, and combined with the sound horizon scale from 7-year \textit{Wilkinson Microwave Anisotropy Probe} $(WMAP7)$ to produce the constraints $\Omega_{m}=0.249 \pm 0.031$ and $w=-0.885 \pm 0.145$. In the second analysis, we used the ACF full shape information to constrain cosmology using real data for the first time, finding $\Omega_{m} = 0.280 \pm 0.022$ and $f_b = \Omega_b/\Omega_m = 0.211 \pm 0.026$. These results are in good agreement with $WMAP7$ findings, showing that the ACF can be efficiently applied to constrain cosmology in future photometric galaxy surveys.

Clustering of luminous red galaxies - IV. Baryon acoustic peak in the line-of-sight direction and a direct measurement ofH(z)

We study the clustering of LRG galaxies in the latest spectroscopic SDSS data releases, DR6 and DR7, which sample over 1 Gpc^3/h^3 to z=0.47. The 2-point correlation function $\xisp$ is estimated as a function of perpendicular $\sigma$ and line-of-sight $\pi$ (radial) directions. We find a significant detection of a peak at $r\simeq 110$Mpc/h, which shows as a circular ring in the $\sigma-\pi$ plane. There is also significant evidence for a peak along the radial direction whose shape is consistent with its originating from the recombination-epoch baryon acoustic oscillations (BAO). A $\xisp$ model with no radial BAO peak is disfavored at $3.2\sigma$, whereas a model with no magnification bias is disfavored at $2\sigma$. The radial data enable, for the first time, a direct measurement of the Hubble parameter $H(z)$ as a function of redshift. This is independent from earlier BAO measurements which used the spherically averaged (monopole) correlation to constrain an integral of $H(z)$. Using the BAO peak position as a standard ruler in the radial direction, we find: $H(z=0.24)= 79.69 \pm 2.32 (\pm 1.29)$ km/s/Mpc for z=0.15-0.30 and $H(z=0.43)= 86.45 \pm 3.27 (\pm 1.69)$ km/s/Mpc for $z=0.40-0.47$. The first error is a model independent statistical estimation and the second accounts for systematics both in the measurements and in the model. For the full sample, $z=0.15-0.47$, we find $H(z=0.34)= 83.80 \pm 2.96 (\pm 1.59)$ km/s/Mpc.