Closing in on α-attractors

Recent observations of cosmic microwave background (CMB) anisotropies combined with large-scale structure may point towards higher values of the scalar spectral index, n_s. This puts previously preferred inflationary models, such as α-attractors, in tension with the new measurements. Pending a resolution of the tension between BAO parameters as determined by CMB datasets and those determined by DESI, we explore in this work the large-n_s regime of α-attractor T-models. We show that some T-models can self-consistently produce an extended reheating stage with a stiff equation of state (w>1/3), which allows values for n_s closer to unity. We employ constraints from P-ACT-LB-BK18 data to illustrate what large-n_s observations might imply for T-models. We show that the n_s measurement yields an upper limit on α that is stronger than the one from the tensor-to-scalar ratio only. We find that n_s is maximised for α~1, therefore the seven Poincaré models are well placed to deliver large n_s. However, the ability of a stiff reheating stage to increase the compatibility of T-models with large-$n_s$ measurements saturates as w->1. Thanks to this effect, we establish that the largest n_s that T-models can produce is n_s=0.9682. T-models are therefore highly predictive in the large-n_s regime and our result provides, under the assumption of perturbative reheating, a benchmark which could be used in the future to rule out T-models.