### Abstract

Measurements of the large-scale structure traced by galaxies, in galaxy redshift surveys, have matured into a critical probe of the underlying cosmological model. Baryon acoustic oscillations (BAO) provide a standard ruler to measure the expansion rate, and redshift space distortions (RSD) allow for an understanding of the growth rate of structure. The current standard procedure to measure baryon acoustic oscillations makes use of a step, to linearise the density field, known as density field reconstruction. This method acts to remove the non-linear damping of the baryon acoustic oscillation peak, due to bulk flows, from the galaxy field. This sharpens the peak in the correlation function and enhances the oscillations in the power spectrum. In cases where it has been applied, reconstruction has offered up to a factor of two improvement in constraining power, dependent on redshift.This thesis makes use of a Fast Fourier Transform (FFT) application of density field reconstruction (Burden et al., 2014, 2015) to perform BAO measurements, test for systematic effects due to assumptions inherent to the current standard analysis and provide a vital component of a novel void galaxy cross-correlation analysis.Density field reconstruction was applied during a reanalysis of the 6-degree Field Galaxy Survey (6dFGS). By combining with post-reconstruction result of the Sloan Digital Sky Survey Main Galaxy Sample (SDSS MGS) (Ross et al., 2015) the currently best distance constraint at z < 0:3 from BAO was provided DV (z

_{eff}) = [539 ± 17] (r

_{s}/r

^{fid}

_{s})Mpc, a ∼3% measurement. This result is consistent with the currently accepted ΛCDM model and fixing the standard ruler using a Ω

_{m}h

^{2}prior from Planck Collaboration et al. (2015) yields a measurement of the Hubble constant of H

_{0}= 64±03:5kms

^{-1}Mpc

^{-1 }(Carter et al., 2018). In the future, both the Dark Energy Spectroscopic Instrument (DESI Collaboration et al., 2016) Bright Galaxy Survey (DESI BGS) and Taipan (da Cunha et al., 2017), will update the BAO constraint in this low redshift regime. These surveys will provide complementary ∼ 1% measurements in the northern and southern hemisphere, respectively. Later in the thesis, reconstruction was applied to mock catalogues for both surveys, demonstrating the potential of these data. Improving distance constraints at low redshift (z < 0:3), to enhance current constraints on H

_{0}, will be crucial to further shed light on the ongoing tension between dierent datasets (Riess et al., 2018; Planck Collaboration et al., 2018).Systematics that could manifest through an incorrect assumption of fiducial cosmology, during the process of BAO measurement, are of critical importance to understand in future surveys, such as DESI and Euclid (Laureijs et al., 2011). These surveys will push the statistical uncertainty on the measurement of the BAO to sub-percent levels, in multiple redshift bins. Using a suite of wCDM simulations, the potential systematic uncertainties were tested across a wide range of cosmologies. This resulted in a negligible effect, of shifting the peak by < 0:1%, suggesting that for the next generation of surveys incorrect assumptions of fiducial cosmology will be unlikely to cause biases in measurements (Carter et al., 2019).Cosmic voids offer an emerging probe of cosmology within Large Scale Structure. Purely linear dynamics can readily describe these low-density environments. As such, they have the potential for being able to decouple the degeneracy between RSD and the Alcock-Paczynski (AP) effect. Valid modelling of the cross-correlation between voids and surrounding galaxies requires the real space position of the voids to be known (Nadathur & Percival, 2019). Although not available from observations directly, a component of density field reconstruction allows for the removal of the linear RSD from the galaxy field, enabling voids to be found in real space. Before applying to data, this method was initially used to model the void-galaxy correlation in the Big MultiDark simulation and consistently recovered the fiducial growth rate to a precision of 3.4% for a (2:5h1Gpc)3 volume (Nadathur et al., 2019a). Following validation, the method was applied directly to the SDSS Baryon Oscillation Spectroscopic Survey (BOSS) twelfth data release in the high redshift CMASS sample. Jointly-fitting for both RSD and AP effects results in a 1% measurement of the AP parameter at z = 0:57, exceeding the precision obtainable from BAO by a factor of ∼ 3:5. Combining the results from the void-galaxy correlation analysis with the BAO and RSD analysis from the same CMASS sample, measurements were made of D

_{A}(0:57)/r

_{s}= 9:383 ± 0:077, H(0:57)r

_{s }= (14:05 ± 0:14)x10

^{3}kms

^{-1}Mpc

^{-1}and fσ8 = 0:453±0:022. These results represent a factor of ∼ 2 improvement over the BOSS CMASS result, excluding voids. Extending to constraining the parameters of both the ΛCDM and extended cosmological models, a sub-optimal combination of probes, including the void analysis, was shown to provide stronger constraining power in comparison to the latest BOSS consensus result (Nadathur et al., 2019b).This thesis combines the work of several projects which tackle different aspects of the field. The overarching theme across these projects is the development and application of density field reconstruction, both in the standard analysis and to provide new uses. The results of this thesis allowed for the optimisation of cosmological measurements available from current and predicted for future galaxy redshift surveys.

Date of Award | Jan 2020 |
---|---|

Original language | English |

Supervisor | Florian Beutler (Supervisor) & Will Percival (Supervisor) |