Current and future constraints on single-field α -attractor models

We study the observational constraints on single-field inflationary models achievable with the next generation of cosmic microwave background (CMB) experiments. We focus on a Stage IV (S4)-like experiment and forecast its constraints on inflationary parameters in the context of α -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 α model a priori. We find that current CMB data are able to place a tight bound on the ratio of the tensor amplitude with the alpha parameter r /α =3.8 7_-0.94^+0.78×10^-3 and on the running of the scalar index α_S=-6. 4_-1.3^+1.6×10^-4 with a value of the scalar index consistent with current constraints. These tight constraints are the result of the strong bound imposed on n_s by the current cosmological data and the theoretical prior of α -attractor models on inflationary observables. This bound can also be translated into an upper bound for α . We find α <25 and α <15 , given r <0.1 and r <0.06 for Planck 2018 and Planck 2018 and BICEP/Keck 2015 data, respectively. In the optimistic scenario of detection of primordial gravitational waves in the CMB B -mode polarization, CMB-S4 will be able to achieve a 15% bound on the value of the α parameter. This bound clearly shows 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 reduces the accuracy on α by about 5%, and thus our main conclusions are still valid. Conversely, in the pessimistic scenario of no detection, a CMB-S4-like experiment will reduce the upper bound on α by around an order of magnitude, leading to a possible exclusion of the Starobinsky model at the level of 6 standard deviations.