Novel Bayesian Inferences from The Cosmic Microwave Background

Abstract

In the evolving landscape of modern precision cosmology, the continuous progress of ongoing and upcoming surveys has provided us with an unprecedented level of statistical power or drawing robust inference. The study of the Cosmic Microwave Background (CMB) fluctuations has been pivotal in this progress. The CMB acts as a tracer of the primordial fluctuation field at the time of the last scattering, around a redshift of $z=1100$, corresponding to 380,000 years after the Big Bang. As these photons have journeyed through the universe, they have experienced weak gravitational lensing by the mass distribution in the large-scale structure of the later universe, thus carrying imprinted information about this later period. Additionally, the frame from which we observe the CMB, specifically the Solar-System barycentre, is in motion relative to the cosmological rest frame, which further influences the observed CMB fluctuations. This thesis explores these two secondary effects on the CMB fluctuations to infer significant phenomena, employing a Bayesian framework to analyze and interpret the data. The first part of the thesis introduces the fundamental concepts of CMB. In the subsequent part, we study the impact of the observation frame's motion on CMB fluctuations. On the largest scales, this motion can boost the CMB monopole to generate a dipole. However, distinguishing this kinematic dipole from an intrinsic dipole in the observed CMB dipole is challenging. According to the simplest and currently most favoured inflationary model, the intrinsic dipolar fluctuation in the CMB, should be of the same order as fluctuations ($10^{-5}$ to $10^{-6}$ K) at smaller angular scales. To test this, we study the relativistic effects of this motion, namely modulation and aberration, on small-scale CMB fluctuations. These effects break the statistical isotropy of the CMB, leading to off-diagonal terms in the harmonic space covariance matrix. We employ a Bayesian approach, using Hamiltonian Monte-Carlo (HMC) sampling, to explore the joint posterior distribution of the covariance matrix and the signal. Our findings align the inferred velocity with the canonical value obtained from the CMB dipole, achieving a significance of approximately $\sim 5\sigma$, the most competitive significance to date. The third part of the thesis focuses on using the gravitational lensing signal of the CMB to probe galaxy clusters. As the largest collapsed objects in the universe, clusters offer critical insights into cosmological parameters. The abundance of clusters as a function of mass and redshift directly probes the structure growth amplitude, mass fraction, neutrino mass, and dark energy equation of state parameters. Hence, accurate cluster mass measurements at high redshifts are crucial for this analysis. Anticipating the CMB Stage 4 (CMB S4) experiment, we demonstrate the effectiveness of maximum-a-posteriori estimation of the gravitational lensing potential for cluster mass estimation. This approach significantly enhances the precision of cluster mass measurements in S4-like experiments by approximately 13-20% over the conventional quadratic estimator (QE). We also address the known bias in the temperature quadratic estimator caused by the strong non-Gaussianity of the signal. Our results show that our estimator effectively mitigates this bias without requiring scale cuts, thus preserving the signal-to-noise ratio.