What is the role of the CMB in providing evidence for inflation, and what information can be extracted from doing CMB power spectra analysis?

Cosmic inflation, proposed to resolve the horizon, flatness, and monopole problems of the standard Big Bang model, remains theoretical without direct observational evidence. This paper investigates the role of the CMB in providing evidence for inflation and examines what cosmological information can be extracted through power spectra analysis. We review how the temperature power spectrum encodes the geometry, matter content, and expansion history of the universe through its acoustic peaks and how CMB polarization (specifically B-mode polarization at large angular scales) would constitute evidence of primordial gravitational waves generated during inflation. We then employ the CMB Analysis Summer School notebook pipeline to simulate CMB maps from theoretical spectra, characterize the impact of instrument noise and foregrounds, apply filtering techniques, and recover power spectra with uncertainties. The analysis demonstrates how raw CMB observations produce cosmological constraints, comparing theoretical predictions with observational cosmology.