# Optimizing Small-scale Redshift Space Distortion Measurements in eBOSS for Cosmological Inference

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## Date

2023-09-21

## Authors

Chapman, Michael

## Advisor

Percival, Will

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## Publisher

University of Waterloo

## Abstract

Modern cosmological datasets have grown substantially in size and the precision of their measurements. While the improvement has had a beneficial impact on our understanding of the cosmological model, it requires equal improvements in our analysis methods and the treatment of systematic biases to achieve optimal results. The model that best fits current observations is a spatially flat model with a cold dark matter (CDM) component that dominates the matter density and a cosmological constant (Λ) that dominates the energy density (ΛCDM). The objective of most cosmological datasets is to precisely measure the parameters of the model, discover an extension, or identify a tension with the expectations from another probe, with the eventual goal of discovering new physics. A probe of particular interest for this thesis is measurements of Redshift Space Distortions (RSD), which constrain the growth of structure through the parameter combination fσ₈, consisting of the logarithmic growth rate of density perturbations, f, and the amplitude of density fluctuations normalized using the standard deviation of fluctuations in a sphere of radius 8 Mpc/h, defined as σ₈. Not only do these measurements constrain core parameters of the ΛCDM model, they are also particularly interesting because they come from the velocity field rather than the density field directly. This makes them complementary to many other large-scale probes, and particularly useful for constraining theories of modified gravity.
One of the new datasets is the extended Baryon Oscillation Spectroscopic Survey (eBOSS), which spectroscopically observed over 1 million galaxies between 2014-2019 as part of the Sloan Digital Sky Survey (SDSS). I present the full eBOSS pipeline, from survey design to the cosmological analysis of the final data release (DR 16), with a focus on my contributions to its development. A key element is the treatment of observational systematics, which must be removed from the data to obtain reliable cosmological results. One of the most significant systematics for small-scale measurements is fibre collisions, where an observational limitation prevents observing close pairs of targets, producing a biased clustering measurement. I present the work of myself and my collaborators within eBOSS to generate Pairwise-Inverse-Probability (PIP) weights and combine them with Angular Upweighting (ANG) to fully remove the effect of fibre collisions, obtaining unbiased clustering measurements on all scales. I also describe my work to correct an observational systematic in the eBOSS Emission Line Galaxy (ELG) sample, caused by inconsistent calibration in the surveys used to identify targets for eBOSS, using a weight-based correction that does not require discarding already observed data. From the final cosmological analyses I present measurements of the Baryon Acoustic Oscillation (BAO) scale and RSD signal from each eBOSS sample. These measurements constrain the expansion history and growth history over the range 0.6 < z < 2.2, finding good agreement with the expectation from the 2018 Planck Cosmic Microwave Background (CMB) data for a flat ΛCDM model. When combined with other SDSS BAO measurements, as well as CMB and supernovae observations, we obtain precise measurements of the curvature of the Universe and the equation-of-state of the dark matter component, two of the simplest possible extensions to the cosmological model, and find both to be in agreement with flat ΛCDM to high precision.
Constraints on fσ₈ using small-scale RSD measurements have a significant statistical advantage over those made on large scales. My collaborators and I measure the small-scale clustering of the DR 16 eBOSS Luminous Red Galaxy (LRG) sample, using the PIP+ANG weights to correct for fibre collisions. We fit to the monopole and quadrupole moments of the 3D correlation function and to the projected correlation function over the separation range 7-60 Mpc/h with a model based on the AEMULUS cosmological emulator to measure fσ₈. We obtain a measurement of fσ₈(z=0.737)=0.408+/-0.038, which is 1.4σ lower than the value expected from Planck 2018 measurements for a flat ΛCDM model, and is more consistent with recent weak-lensing measurements. The level of precision achieved is 1.7 times better than more standard measurements made using only the large-scale modes of the same sample. We also fit to the data using the full range of scales modelled by the AEMULUS cosmological emulator, 0.1-60 Mpc/h, and find a 4.5σ tension in the amplitude of the halo velocity field with the Planck+ΛCDM model, driven by a mismatch on the non-linear scales. We perform a robust analysis of possible sources of systematics, including the effects of redshift uncertainty and incompleteness due to target selection that were not included in previous analyses fitting to clustering measurements on small scales.
The restriction of constraining fσ₈ using only the measurement scales 7-60 Mpc/h was motivated by the minimum scale at which the velocity scaling parameter used in the emulator to replicate changes in the growth rate still matched the expectation for a change in fσ₈. This issue highlights an important concern for small-scale RSD measurements: the need to carefully disentangle the linear and non-linear information when interpreting RSD in terms of fσ₈. It is particularly important to do this given the significant deviation from the expectation based on the Planck+ΛCDM model derived using the full range of scales modelled by the emulator in the previous analysis. We construct a new emulator-based model for small-scale galaxy clustering with scaling parameters for both the linear and non-linear velocities of galaxies, allowing us to isolate the linear growth rate. We train the emulator using simulations from the AbacusCosmos suite, estimating the linear velocity of galaxies by evolving the velocities of the simulations' Zel'dovich approximation initial conditions using linear growth. We apply a tophat smoothing kernel of radius 5 Mpc/h to the field to remove the remaining small-scale velocity dispersion, finding good agreement between the behaviour of our linear velocity scaling parameter and the expectation for a change in fσ₈ on all scales. We apply the new emulator to the eBOSS LRG sample, obtaining a value of fσ₈(z=0.737)=0.368+/-0.041, in 2.3σ tension with the Planck+ΛCDM expectation. We also find less dependence on the minimum measurement scale than the previous analysis, validating our improved emulator.
The small- and large-scale eBOSS results provide a precise test of ΛCDM from both the expansion and growth history. While consistent with ΛCDM, these measurements give interesting insight into the current H₀ and S₈ tensions between various cosmological probes, and give some evidence for a third tension between the fσ₈ measurements of small-scale RSD analyses and the Planck 2018+ΛCDM expectation. The observations and analysis of the eBOSS samples, particularly the treatment of observational systematics, pave the way for the next generation of surveys, such as those currently being done by the Dark Energy Spectroscopic Instrument (DESI) and Euclid space mission. Applying the small-scale RSD analysis method to these surveys will be critical to achieving optimal constraints, which have the potential to revolutionize the ΛCDM model and our understanding of the Universe.

## Description

## Keywords

cosmological parameters, galaxy redshifts and distances, observational cosmology, large-scale structure of the Universe, astrophysics, cosmology