Confronting K\"ahler moduli inflation with CMB data

In models of inflation obtained from string compactification, moduli vacuum misalignment leads to an epoch in the post-inflationary history of the universe when the energy density is dominated by cold moduli particles. This effect leads to a modification in the number of $e$-foldings ($N_{\mathrm{p}\mathrm{i}\mathrm{v}\mathrm{o}\mathrm{t}}$) between horizon exit of the CMB modes and the end of inflation. Taking K"ahler moduli inflation as a prototype, the shift in $e$-foldings turns out to be a function of the model parameters which also determines the inflationary observables. We analyse this scenario numerically using publicly available {\sc{ModeChord}} and {\sc{CosmoMC}} with the latest \emph{Planck+BICEP2/Keck array} data to constrain the model parameters and $N_{\mathrm{p}\mathrm{i}\mathrm{v}\mathrm{o}\mathrm{t}}$. In light of the present and future precision data, the results show the importance of careful consideration of any post-inflationary non-standard epoch, as well as of the effects of reheating.