Current and Future constraints on single-field $\alpha$-Attractor model
  We study here the observational constraints on single-field inflationary
models achievable with the next generation of CMB experiments. We particularly
focus on a Stage-IV like experiment and forecasts its constraints on
inflationary parameters in the context of $\alpha$-attractor inflation
comprising a large class of single-field models. To tailor our forecasts we use
as a fiducial model the results obtained with current CMB and LSS data,
assuming the $\alpha$-model a priori. We found that current CMB data are able
to place a tight bound on the ratio of the tensor-to-scalar ratio with the
alpha parameter $r/\alpha = 3.87^{+0.78}_{-0.94}\cdot 10^{-3}$ and on the
running of the scalar index $\alpha_S = -6.4^{+1.6}_{-1.3}\cdot 10^{-4}$ with a
value of the scalar index consistent with current constraints. In the
optimistic scenario of detection of primordial gravitational waves in the CMB
B-mode polarization power spectra, we found that CMB-S4 will be able to achieve
a $15\%$ bound on the value of the parameter $\alpha = 1.01^{+0.14}_{-0.18}$.
This bound clearly show the ability of CMB-S4 to constrain not only the energy
scale of inflation but also the shape of its potential. Enlarging the baseline
model to also include the neutrino sector merely reduce the accuracy of $5\%$
leading to $\alpha = 1.07^{+0.18}_{-0.23}$ so that our main conclusions are
still valid.
