Inflation : connecting theory to observation
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The inflationary paradigm has become widely accepted as an accurate framework in which to describe the physics of the early universe, due both to the conceptual advantages of the idea and the agreement of its predictions with observational data. However, it remains to be determined which of the many detailed theories of inflation correctly describe the universe in which we live. Any such theory faces the challenge of making accurate predictions which agree with observation while also fitting consistently into a theory of high energy physics. Within this challenge there exists the great opportunity to constrain speculative models of fundamental physics. Inflation thereby provides an observational window into theories conventionally thought to be unreachable by experiment. Measurements of anisotropies in the cosmic microwave background radiation and the distribution of large scale structure have proved to be invaluable tools to probe inflation. There has been recent interest in examining the deviations from gaussianity in the statistics of the observed fluctuations. These higher order statistics, if conclusively discovered, stand to teach us a great deal about inflation. Forthcoming data including improved measurements of the cosmic microwave background temperature and polarization will provide additional means to investigate the inflationary era. It is important to understand precisely what impact inflation has had on the universe we observe and thus understand precisely what observation can tell us about inflation and how it may fit into a fundamental theory of physics. We will show the conditions under which the cosmological correlation functions generated during inflation are conserved, and thus identify the conditions which allow us to use observations today to learn about inflation. We first prove a general result which applies only to the leading approximation of the correlation functions, and then we discuss how to treat the additional complications that come with subleading corrections. Next, we will discuss the observational implications of achieving the conditions for conservation for a particular class of inflationary models. Lastly, we discuss one example of how observations can be used to probe non-inflationary physics beyond the standard cosmological model.