Contributed chapter to " Proceedings of the New Cosmology Summer School" edt. M. Colless, to be published by World Scientific, 2003. Based on five lectures given at the 16th Canberra International Summer School "The New Cosmology" held 3-14 February at the Australian National University.
astro-ph/0305179

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Abstract. I present a pedagogical review of inflation and the cosmic microwave background. I describe how a short period of accelerated expansion can replace the special initial conditions of the standard big bang model. I also describe the development of CMBology: the study of the cosmic microwave background. This cool (3 K) new cosmological tool is an increasingly precise rival and complement to many other methods in the race to determine the parameters of the Universe: its age, size, composition and detailed evolution.

Table of Contents

A NEW COSMOLOGY

Progress

Big Bang: Guilty of Not Having an Explanation

TUNNEL VISION: THE INFLATIONARY SOLUTION

Friedmann-Robertson-Walker metric -> Hubble's law and Cosmic Event Horizons

Inflationary Expansion: The Magic of a Shrinking Comoving Event Horizon

FRIEDMANN OSCILLATIONS: THE RISE AND FALL OF DOMINANT COMPONENTS

Friedmann's Equation -> Exponential Expansion

INFLATIONARY SOLUTIONS TO THE FLATNESS AND HORIZON PROBLEMS

What is the Flatness Problem?

Solving the Flatness Problem

Horizon problem

How big is a causally connected patch of the CMB without and with inflation?

HOW DOES INFLATION PRODUCE ALL THE STRUCTURE IN THE UNIVERSE?

THE STATUS OF INFLATION

Inflationary Observables

CMB

History

What is the CMB?

Spectrum

Where did the energy of the CMB come from?

Dipole

Anisotropies

What are the oldest fossils we have from the early universe?

Observational Constraints from the CMB

Background and the Bumps on it and the Evolution of those Bumps

The End of Cosmology?

Tell me More

REFERENCES