RSD measurements from BOSS galaxy power spectrum using the halo perturbation theory model

We present growth of structure constraints from the cosmological analysis of the power spectrum multipoles of SDSS-III BOSS DR12 galaxies. We use the galaxy power spectrum model of Hand et al. (2017), which decomposes the galaxies into halo mass bins, each of which is modeled separately using the relations between halo biases and halo mass. The model combines Eulerian perturbation theory and halo model calibrated on $N$-body simulations to model the halo clustering. In this work, we also generate the covariance matrix by combining the analytic disconnected part with the empirical connected part: we smooth the connected component by selecting a few principal components and show that it achieves good agreement with the mock covariance. Our analysis differs from recent analyses in that we constrain a single parameter $f\sigma_8$ fixing everything else to Planck+BAO prior, thereby reducing the effects of prior volume and mismodeling. We find tight constraints on $f\sigma_8$: $f\sigma_8(z_{\mathrm{eff}}=0.38)=0.489 \pm 0.038$ and $f\sigma_8(z_{\mathrm{eff}}=0.61)=0.455 \pm 0.028$ at $k_{\mathrm{max}} = 0.2\ h$Mpc$^{-1}$, with an overall amplitude error of 5(within 0.3 sigma) of Planck amplitude. We discuss the sensitivity of cosmological parameter estimation to the choice of scale cuts, covariance matrix, and the inclusion of hexadecapole$P_4(k)$. We show that with$k_{\mathrm{max}} = 0.4\ h$Mpc$^{-1}$the constraints improve considerably to an overall 3.2misspecification on MultiDark-PATCHY mocks. Choosing$k_{\mathrm{max}}$ consistently and reliably remains the main challenge of RSD analysis methods.Comment: 21 pages, 13 figure

Towards Neutrino Mass from Cosmology without Optical Depth Information

With low redshift probes reaching unprecedented precision, uncertainty of the CMB optical depth is expected to be the limiting factor for future cosmological neutrino mass constraints. In this paper, we discuss to what extent combinations of CMB lensing and galaxy surveys measurements at low redshifts $z\sim 0.5-5$ will be able to make competitive neutrino mass measurements without relying on any optical depth constraints. We find that the combination of LSST galaxies and CMB-S4 lensing should be able to achieve constraints on the neutrino mass sum of 25meV without optical depth information, an independent measurement that is competitive with or slightly better than the constraint of 30meV possible with CMB-S4 and present-day optical depth measurements. These constraints originate both in structure growth probed by cross-correlation tomography over a wide redshift range as well as, most importantly, the shape of the galaxy power spectrum measured over a large volume. We caution that possible complications such as higher-order biasing and systematic errors in the analysis of high redshift galaxy clustering are only briefly discussed and may be non-negligible. Nevertheless, our results show that new kinds of high-precision neutrino mass measurements at and beyond the present-day optical depth limit may be possible.Comment: 8 pages, 6 figure

Application of Bayesian Methods in Cosmological Data Analysis: Parameter Constraint Forecasts for Stage-IV Surveys and Bayesian Large-Scale Structure Inference

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