3.2 Cosmic Inflation 30 scales, it is clear that this must break down at some level, in order to fa- cilitate the existence of stars, galaxies and humans! In addition, when we look at the CMB, we see tiny perturbations in the temperature across the sky. What mechanism was responsible for producing the associated density perturbations in the very early Universe? We now discuss one of the key areas of Particle Cosmology in the 21 st century and indeed the main topic of work in this thesis: Cosmic Inflation. Firstly, let us define inflation. With regard to the scale factor a ( t ), inflation is defined as any period of spacetime expansion in which we have We therefore have a period of “repulsive gravity”. Another, extremely im- portant, definition of inflation is This defines inflation as a period of expansion in which the comoving Hubble length is decreasing. Another definition of inflation, in terms of the time evolution of the Hubble parameter, is − ˙ H H 2 < 1 (3.14) d d t H − 1 a < 0 (3.13) ¨ a > 0 (3.12) 3.2 Cosmic Inflation