What is the most we can ever hope to infer about the nature of inflaton if all we ever end up inferring from observations are correlation functions of the adiabatic perturbation $\mathcal R$? At the level of the two-point function, the answer is not as much as we'd like. There are many degeneracies (and even dualities between very different cosmological backgrounds) that limit our ability to infer the background evolution, and by extension, to learn anything about the true nature of the inflaton. Of course, detecting tensor modes would help us a long way in understanding the character of inflation, but what if a positive detection remains elusive?
In this talk we will elaborate on how features, if present in the primordial power spectrum (possibly at scales we have yet to observe),  allow us a powerful probe into physics that underlies, or is beyond the cosmological standard model. Detecting such features would not only allow us to infer new characteristic scales that encode the physical realization of inflation, they also generate correlated features in higher n-point functions of $\mathcal R$. These correlations are a direct consequence of the effective field theory expansion of $\mathcal R$ which non-linearly realizes the breaking of time translational invariance by slow roll. The observation of such correlations between different n-point spectra over a range of e-folds would directly confirm the nature of inflaton as an effectively single light scalar degree of freedom embedded in a theory that is UV completable, and would allow us to infer appropriately limited information about this completion. We discuss the prospects for observing such correlations in future LSS and 21cm observations.