Loops in inflationary correlation functions
  We review the recent progress regarding the loop corrections to the
correlation functions in the inflationary universe. A naive perturbation theory
predicts that loop corrections generated during inflation suffer from various
infrared (IR) pathologies. Introducing an IR cutoff by hand is not only
unsatisfactory but also does not fix the problem of secular growth, which may
ruin the predictive power of inflation models if the inflation lasts
sufficiently long. We discuss the origin of the IR divergences and explore the
regularity conditions of loop corrections for the adiabatic perturbation, the
iso-curvature perturbation, and the tensor perturbation, in turn. These three
kinds of perturbations have qualitative differences, but in discussing the IR
regularity there is a feature common to all cases, which is the importance of
the proper identification of observable quantities. Genuinely observable
quantities should respect the gauge invariance from the view point of a local
observer. Interestingly, we find that the requirement of the IR regularity
restricts the allowed quantum states.
