Closing in on α -attractors

Abstract 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 ( w̅ > 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 with monomial potentials. 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 w̅ → 1. Thanks to this effect, we establish that the largest n s that monomial 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 monomial T-models.