Wandering in the Background: A CMB Explorer
Wayne Hu
TL;DR
This work presents a comprehensive, relativistic treatment of CMB distortions and anisotropies, deriving how spectral distortions ($\mu$, $y$) and temperature fluctuations encode the universe’s thermal history and dynamics. By combining a full Boltzmann framework with multifluid perturbation theory and careful gauge choices, it links acoustic physics in the photon-baryon fluid to observable $C_\ell$ features, ISW effects, and diffusion damping, across open, flat, and $\Lambda$-dominated cosmologies. It also quantifies the impact of reionization, spectral thermalization processes, and potential decays on the CMB spectrum, aligning theoretical predictions with FIRAS constraints to bound early-universe energy injection and the primordial power spectrum. The results establish CMB observations as precise probes of fundamental cosmological parameters, baryon content, and the nature of initial perturbations, with implications for structure formation and the geometry of the universe.
Abstract
We develop and examine the principles governing the formation of distortions in the cosmic microwave background. Distortions in the frequency or spectral distribution of the background probe the thermal history of the universe whereas those in the angular temperature distribution probe its dynamics and geometry. Stressing model independent results, we show how the microwave background can be used to extract information on the mass density, vacuum density, baryon content, radiation content, expansion rate and some aspects of structure formation in the universe. To address these issues, we systematically develop relativistic kinetic and perturbation theory addressing issues such as fluctuation representation, or gauge, normal mode analysis in an open geometry, and second order effects. Through analytic and numerical results, we construct anisotropies in a critical, open, or cosmological constant universe with adiabatic and/or isocurvature initial conditions allowing for possible early reionization. We find that anisotropy formation is a simple process governed by the Compton scattering of photons and electrons and their gravitational coupling to the other particle species in the universe.