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Register a new userA Study on the Baryon Acoustic Oscillation with Topological Data Analysis
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(abridged) The scale of the acoustic oscillation of baryons at the baryon-photon decoupling is imprinted on the spatial distribution of galaxies in the Universe, known as the baryon acoustic oscillation (BAO). The correlation functions and power spectrum are used as a central tool for the studies on the BAO analysis. In this work, we analyzed the spatial distribution of galaxies with a method from the topological data analysis (TDA), in order to detect and examine the BAO signal in the galaxy distribution. The TDA provides a method to treat various types of holes in point set data, by constructing the persistent homology (PH) group from the geometric structure of data points and handling the topological information of the dataset. We can obtain the information on the size, position, and statistical significance of the holes in the data. A particularly strong point of the persistent homology is that it can classify the holes by their spatial dimension, i.e., a 0-dim separation, 1-dim loop, 2-dim shell, etc. We first analyzed the simulation datasets with and without the baryon physics to examine the performance of the PH method. We found that the PH is indeed able to detect the BAO signal: simulation data with baryon physics present a prominent signal from the BAO, while data without baryon physics does not show this signal. Then, we applied the PH to a quasar sample at $z <1.0$ from extended Baryon Oscillation Spectroscopic Survey in Sloan Digital Sky Survey Data Release 14. We discovered a characteristic hole (a hollow shell) at a scaler $sim150 [{rm Mpc}]$. This exactly corresponds to the BAO signature imprinted in the galaxy/quasar distribution. We performed this analysis on a small subsample of 2000 quasars. This clearly demonstrates that the PH analysis is very efficient in finding this type of topological structures even if the sampling is very sparse.
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We define Baryon Acoustic Oscillation (BAO) distances $hat{d}_alpha(z, z_c)$, $hat{d}_z(z, z_c)$, and $hat{d}_/(z, z_c)$ that do not depend on cosmological parameters. These BAO distances are measured as a function of redshift $z$ with the Sloan Digital Sky Survey (SDSS) data release DR12. From these BAO distances alone, or together with the correlation angle $theta_textrm{MC}$ of the Cosmic Microwave Background (CMB), we constrain the cosmological parameters in several scenarios. We find $4.3 sigma$ tension between the BAO plus $theta_textrm{MC}$ data and a cosmology with flat space and constant dark energy density $Omega_textrm{DE}(a)$. Releasing one and/or the other of these constraints obtains agreement with the data. We measure $Omega_textrm{DE}(a)$ as a function of $a$.
We measure the baryon acoustic oscillation (BAO) observables $hat{d}_alpha(z, z_c)$, $hat{d}_z(z, z_c)$, and $hat{d}_/(z, z_c)$ as a function of redshift $z$ in the range 0.1 to 0.7 with Sloan Digital Sky Survey (SDSS) data release DR13. These observables are independent and satisfy a consistency relation that provides discrimination against miss-fits due to background fluctuations. From these measurements and the correlation angle $theta_textrm{MC}$ of fluctuations of the Cosmic Microwave Background (CMB) we obtain $Omega_k = -0.015 pm 0.030$, $Omega_{textrm{DE}} + 2.2 Omega_k = 0.717 pm 0.004$ and $w_1 = 0.37 pm 0.61$ for dark energy density allowed to vary as $Omega_{textrm{DE}}(a) = Omega_{textrm{DE}} [ 1 + w_1 ( 1 - a)]$. We present measurements of $Omega_{textrm{DE}}(a)$ at six values of the expansion parameter $a$. Fits with several scenarios and data sets are presented. The data is consistent with space curvature parameter $Omega_k = 0$ and $Omega_{textrm{DE}}(a)$ constant.
We define Baryon Acoustic Oscillation (BAO) observables $hat{d}_alpha(z, z_c)$, $hat{d}_z(z, z_c)$, and $hat{d}_/(z, z_c)$ that do not depend on any cosmological parameter. From each of these observables we recover the BAO correlation length $d_textrm{BAO}$ with its respective dependence on cosmological parameters. These BAO observables are measured as a function of redshift $z$ with the Sloan Digital Sky Survey (SDSS) data release DR12. From the BAO measurements alone, or together with the correlation angle $theta_textrm{MC}$ of the Cosmic Microwave Background (CMB), we constrain the curvature parameter $Omega_k$ and the dark energy density $Omega_textrm{DE}(a)$ as a function of the expansion parameter $a$ in several scenarios. These observables are further constrained with external measurements of $h$ and $Omega_textrm{b} h^2$. We find some tension between the data and a cosmology with flat space and constant dark energy density $Omega_textrm{DE}(a)$.
Extraction of the Baryon Acoustic Oscillations (BAO) to percent level accuracy is challenging and demands an understanding of many potential systematic to an accuracy well below 1 per cent, in order ensure that they do not combine significantly when compared to statistical error of the BAO measurement. Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) SDSS Data Release Eleven (DR11) reaches a distance measurement with $sim 1%$ statistical error and this prompts an extensive search for all possible sub-percent level systematic errors which could be safely ignored previously. In this paper, we analyze the potential systematics in BAO fitting methodology using mocks and data from BOSS DR10 and DR11. We demonstrate the robustness of the fiducial multipole fitting methodology to be at $0.1%-0.2%$ level with a wide range of tests in mock galaxy catalogs pre- and post-reconstruction. We also find the DR10 and DR11 data from BOSS to be robust against changes in methodology at similar level. This systematic error budget is incorporated into the the error budget of Baryon Oscillation Spectroscopic Survey (BOSS) DR10 and DR11 BAO measurements. Of the wide range of changes we have investigated, we find that when fitting pre-reconstructed data or mocks, the following changes have the largest effect on the best fit values of distance measurements both parallel and perpendicular to the line of sight: (a) Changes in non-linear correlation function template; (b) Changes in fitting range of the correlation function; (c) Changes to the non-linear damping model parameters. The priors applied do not matter in the estimates of the fitted errors as long as we restrict ourselves to physically meaningful fitting regions.[abridged]
We derive constraints on cosmological parameters and tests of dark energy models from the combination of baryon acoustic oscillation (BAO) measurements with cosmic microwave background (CMB) and Type Ia supernova (SN) data. We take advantage of high-precision BAO measurements from galaxy clustering and the Ly-alpha forest (LyaF) in the BOSS survey of SDSS-III. BAO data alone yield a high confidence detection of dark energy, and in combination with the CMB angular acoustic scale they further imply a nearly flat universe. Combining BAO and SN data into an inverse distance ladder yields a 1.7% measurement of $H_0=67.3 pm1.1$ km/s/Mpc. This measurement assumes standard pre-recombination physics but is insensitive to assumptions about dark energy or space curvature, so agreement with CMB-based estimates that assume a flat LCDM cosmology is an important corroboration of this minimal cosmological model. For open LCDM, our BAO+SN+CMB combination yields $Omega_m=0.301 pm 0.008$ and curvature $Omega_k=-0.003 pm 0.003$. When we allow more general forms of evolving dark energy, the BAO+SN+CMB parameter constraints remain consistent with flat LCDM. While the overall $chi^2$ of model fits is satisfactory, the LyaF BAO measurements are in moderate (2-2.5 sigma) tension with model predictions. Models with early dark energy that tracks the dominant energy component at high redshifts remain consistent with our constraints. Expansion history alone yields an upper limit of 0.56 eV on the summed mass of neutrino species, improving to 0.26 eV if we include Planck CMB lensing. Standard dark energy models constrained by our data predict a level of matter clustering that is high compared to most, but not all, observational estimates. (Abridged)
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