## Contents 

I. Introduction 8 

II. Inflation 12 

A. Slow-roll inflation 12 

B. Primordial density perturbations 14 

1. Fluctuations in de Sitter 15 

2. Adiabatic perturbations and the Sachs-Wolfe effect 15 

3. Spectrum of adiabatic perturbations 18 

4. Gravitational waves 20 

C. Multi-field perturbations 21 

1. Adiabatic and isocurvature conditions 22 

2. Adiabatic perturbations due to multi-field 22 

3. Isocurvature perturbations and CMB 23 

4. Non-Gaussianity 24 

D. Curvaton and fluctuating inflaton coupling/mass scenarios 25 

E. Confrontation to the CMB and other observational data 28 

1. Primordial power spectrum for scalar and tensor 28 

2. Cosmic strings and CMB fluctuations 30 

3. Isocurvature perturbations 31 

4. Higher order correlation functions 32 

F. Dynamical challenges for inflation 33 

1. Initial conditions for inflation 33 

2. Choice of a vacuum where inflation ends 36 

3. Quantum to classical transition 36 

4. Inflaton decay, reheating and thermalization 37 

G. Requirements for a successful inflation 38 

1. Baryons and nucleosynthesis 38 

2. Baryogenesis 39 

3. Cold dark matter 40 

III. Particle physics tools for inflation 41 

