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The Standard Model of Cosmology has successfully predicted the nucleosynthesis of the light elements, the existence of the cosmic background radiation, and the dynamics of an expanding universe, i.e. the Hubble expansion. However, this model can not account for a number of initial value problems, such as the flatness and monopole problems. Inflationary cosmology resolves these concerns, while preserving the successes of the Big-Bang model. Inflation was originally introduced for this reason and its motivation relied on predictions from particle theory. In more recent times, inflation has been abstracted to a much more general theory. It continues to resolve the initial value problems, but also offers an explanation of the observed large-scale structure of the universe.

In this paper, the fundamentals of modern cosmology for an isotropic and homogeneous space-time, which is naturally motivated by observation, will be reviewed. The Friedmann equations are derived and the consequences for the dynamics of the universe are discussed. A brief introduction to the thermal properties of the universe is presented as motivation for a discussion of the horizon problem. Moreover, other issues suggesting a more general theory are presented and inflation is introduced as a resolution to this conundrum.

Inflation is shown to actually exist as a scenario, rather than a specific model. In the most general case one speaks of the inflaton field and its corresponding energy density. Models of inflation differ in their predictions and the corresponding evolution of an associated inflaton field can be explored in a cosmological context. The equations of motion are cast in a form that makes observational consequences manifest. The slow-roll approximation (SRA) is discussed as a more tractable and plausible evolution for the inflaton field and the slow-roll parameters are defined. Using the SRA, inflation predicts a near-Gaussian adiabatic perturbation spectrum resulting from quantum fluctuations in the inflaton field and the DeSitter space-time metric. These result in a predicted power spectrum of gravity waves and temperature anisotropies in the cosmic background, both of which will be detectable in future experiments.

Inflation is shown to be a rigorous theory that makes concise predictions in regards to a needed inflaton potential at the immediate Post-Planck or perhaps even the Planck epoch (~ 10-43 s). This offers the exciting possibility that inflation can be used to predict new particle physics or serve as a constraint for phenomenology from theories such as Superstring theory.

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