Inflation and the Theory of Cosmological Perturbations

TL;DR

The lectures introduce inflation as a solution to the horizon, flatness, and entropy problems, and show how quantum fluctuations during (quasi) de Sitter inflation generate primordial cosmological perturbations that seed CMB anisotropies and large-scale structure. The core approach uses gauge-invariant variables such as the comoving curvature perturbation ${\cal R}$ and the Mukhanov variable $u$ to derive the scalar and tensor perturbation spectra, obtaining ${\cal P}_{\cal R}(k)$ with ${n_{\cal R}}-1 = 2\eta - 6\epsilon$ and ${\cal P}_T(k)$ with ${n_T} = -2\epsilon$, plus the tensor-to-scalar ratio $r = 16\epsilon$ and the consistency relation $r = -8 n_T$. The work also discusses reheating, preheating, and transfer of perturbations to radiation, as well as the curvaton mechanism and isocurvature and non-Gaussianity that can arise in multi-field scenarios. Finally, it highlights observational implications for CMB and gravitational waves, emphasizing that B-mode polarization measurements can probe the inflation scale and test the single-field consistency relations.

Abstract

These lectures provide a pedagogical introduction to inflation and the theory of cosmological perturbations generated during inflation which are thought to be the origin of structure in the universe.

Figures (1)

• Figure 1: The CMB radiation projected onto a sphere