UC Berkeley

The application of Bayesian methodology in cosmological data analysis has gained enormous popularity, as the Bayesian interpretation of statistics is particularly appealing to the field of cosmology in which its subject, the Universe, is unique. In the coming decade, unprecedented size of data observed from forthcoming Stage-IV experiments - e.g. galaxy surveys such as DESI, Euclid, Roman, and LSST and CMB surveys such as SO and CMB-S4 - will call for the development of more advanced statistical analysis tools, and the Bayesian framework is expected to provide a key to decoding information hidden in the dataset. This will enable us to unlock the fundamental mysteries of the Universe, which include the nature of dark matter and energy, the neutrino mass scale, and inflationary physics.

Within a Bayesian framework, this thesis develops numerical and statistical tools in preparation for Stage-IV cosmological surveys. First, we forecast the constraining power of combining LSST clustering and CMB-S4 lensing; we find that the constraint on the neutrino mass sum of 25meV can be achieved without optical depth information, and its constraint on the dark energy equation of state parameter is comparable to the LSST tomographic cosmic shear forecast. In the remainder of this thesis, we build an efficient, reliable analysis pipeline for growth of structure measurements from large-scale structure dataset, which can be useful for upcoming galaxy redshift surveys. This includes: hybrid covariance matrix generated by integrating the analytic disconnected part and the data-driven connected part, optimization-based numerical method for posterior inference, and the use of the halo perturbation theory model to provide RSD measurements from the power spectrum multipoles of SDSS-III BOSS DR12 galaxies. With the pipeline developed in this thesis, we find a tight constraint on $f\sigma_8$ corresponding to $S_8 = 0.821 \pm 0.037$ or an overall amplitude error of 4\% at $k_{\mathrm{max}} = 0.2\ h$Mpc$^{-1}$, within 0.3 sigma of Planck's $S_8 = 0.832 \pm 0.013$. We also show that on smaller scales ($k_{\mathrm{max}} = 0.4\ h$Mpc$^{-1}$) the constraint improves considerably to an overall 2.7\% amplitude error (with $S_8 = 0.786 \pm 0.021$), but there is some evidence of model misspecification. Such RSD measurements provide one of the most powerful cosmological probes by testing dark energy and different gravity models. Finally, we discuss the fundamental plane effect, which is claimed to be an important systematics of RSD analyses, and show that its impact on growth of structure constraints is insignificant.