Current and future constraints on single-field <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math> -attractor models

We study the observational constraints on single-field inflationary models achievable with next generation of cosmic microwave background (CMB) experiments. focus a Stage IV (S4)-like experiment and forecast its parameters in context $\ensuremath{\alpha}$-attractor inflation comprising large class models. To tailor our forecasts, we use as fiducial model results obtained current CMB LSS data, assuming $\ensuremath{\alpha}$ priori. find that data are able to place tight bound ratio tensor amplitude alpha parameter $r/\ensuremath{\alpha}=3.8{7}_{\ensuremath{-}0.94}^{+0.78}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ running scalar index ${\ensuremath{\alpha}}_{S}=\ensuremath{-}6.{4}_{\ensuremath{-}1.3}^{+1.6}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ value consistent constraints. These result strong imposed ${n}_{s}$ by cosmological theoretical prior observables. This can also be translated into an upper for $\ensuremath{\alpha}$. $\ensuremath{\alpha}&lt;25$ $\ensuremath{\alpha}&lt;15$, given $r&lt;0.1$ $r&lt;0.06$ Planck 2018 BICEP/Keck 2015 respectively. In optimistic scenario detection primordial gravitational waves $B$-mode polarization, CMB-S4 will achieve 15% parameter. clearly shows ability constrain not only energy scale but shape potential. Enlarging baseline include neutrino sector merely reduces accuracy about 5%, thus main conclusions still valid. Conversely, pessimistic no detection, CMB-S4-like reduce around order magnitude, leading possible exclusion Starobinsky at level 6 standard deviations.