A generic feature of inflationary models in supergravity/string constructions is vacuum misalignment for the moduli fields. The associated production of moduli particles leads to an epoch in the post-inflationary history in which the energy density is dominated by cold moduli particles. This modification of the post-inflationary history implies that the preferred range for the number of e-foldings between horizon exit of the modes relevant for CMB observations and the end of inflation (Nk) depends on moduli masses. This in turn implies that the precision CMB observables ns and r are sensitive to moduli masses. We analyse this sensitivity for some representative models of inflation and find the effect to be highly relevant for confronting inflationary models with observations.
Das, K., Dutta, K., & Maharana, A. (2015). Inflationary predictions and moduli masses. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 751, 195–200. https://doi.org/10.1016/j.physletb.2015.10.041