In this talk, we investigate what it precisely means that we may integrate out the massive degrees of freedom in the computation of primordial density perturbations. We first study the case of direct coupling. Then, we study the universal gravitational coupling. In the former case, we find results consistent with the conventional wisdom, while in the latter case, we find that such a contribution has several unusual properties: it does not decrease as the mass of the spectator field increases; it has a significant size and cannot be turned off by any adjustable parameters; and it applies to all massive scalars existed during inflation, making the overall effect unexpectedly large. As a result, the primordial density perturbations turns out to be anomalously sensitive to the high energy physics.
