Massive Fields as Systematics for Single Field Inflation

During inflation, massive fields can contribute to the power spectrum of curvature perturbation via a dimension-5 operator. This contribution can be considered as a bias for the program of using $n_s$ and $r$ to select inflation models. Even the dimension-5 operator is suppressed by $\mathrm{\Lambda }=M_p$, there is still a significant shift on the $n_s$-$r$ diagram if the massive fields have $m\sim H$. On the other hand, if the heavy degree of freedom appears only at the same energy scale as the suppression scale of the dimension-5 operator, then significant shift on the $n_s$-$r$ diagram takes place at $m=\Lambda \sim 70H$, which is around the inflationary time-translation symmetry breaking scale. Hence, the systematics from massive fields pose a greater challenge for future high precision experiments for inflationary model selection. This result can be thought of as the impact of UV sensitivity to inflationary observables.