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Register a new userStudy of baryon acoustic oscillations with SDSS DR13 data and measurements of $Omega_k$ and $Omega_textrm{DE}(a)$
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B. Hoeneisen
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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.
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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 $Omega_textrm{DE}(a)$.
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 $a$.
From Baryon Acoustic Oscillation measurements with Sloan Digital Sky Survey SDSS DR14 galaxies, and the acoustic horizon angle $theta_*$ measured by the Planck Collaboration, we obtain $Omega_m = 0.2724 pm 0.0047$, and $h + 0.020 cdot sum{m_ u} = 0.7038 pm 0.0060$, assuming flat space and a cosmological constant. We combine this result with the 2018 Planck `TT,TE,EE$+$lowE$+$lensing analysis, and update a study of $sum m_ u$ with new direct measurements of $sigma_8$, and obtain $sum m_ u = 0.27 pm 0.08$ eV assuming three nearly degenerate neutrino eigenstates. Measurements are consistent with $Omega_k = 0$, and $Omega_textrm{de}(a) = Omega_Lambda$ constant.
(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.
Baryon Acoustic Oscillations (BAO) are frozen relics left over from the pre-decoupling universe. They are the standard rulers of choice for 21st century cosmology, providing distance estimates that are, for the first time, firmly rooted in well-understood, linear physics. This review synthesises current understanding regarding all aspects of BAO cosmology, from the theoretical and statistical to the observational, and includes a map of the future landscape of BAO surveys, both spectroscopic and photometric.
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