Viability of generalized α-inflation from Planck, ACT, and DESI Data

We study inflationary constraints from reheating on two classes of single-field inflationary models: a generalized [Formula: see text]-attractor with potential [Formula: see text] and the [Formula: see text]-Starobinsky model with potential [Formula: see text]. Using a semi-analytical relation that connects inflationary dynamics to reheating, we solve for the horizon-crossing field value and calculate the scalar spectral index [Formula: see text], the tensor-to-scalar ratio [Formula: see text], and the reheating temperature [Formula: see text]. We consider three perturbative decay channels of the inflaton: gravitational, Yukawa (fermionic), and scalar. The parameter space spanned by [Formula: see text] for the first model and [Formula: see text] for the second is explored and compared with recent measurements from Planck and ACT DR6, as well as BAO from DESI DR2. For clarity, we emphasize that ACT DR6 alone is fully compatible with Planck regarding [Formula: see text]. The upward shift toward [Formula: see text] appears only when DESI DR2 BAO are combined with CMB datasets (Planck+DESI, ACT+DESI, SPT-3G+DESI), and is likewise seen in the P–ACT–LB2+DESI combination. CMB-only combinations (e.g., Planck+ACT or Planck+ACT+SPT-3G) primarily refine constraints and do not by themselves raise [Formula: see text]. Our comparisons and model assessments are therefore made with this distinction in mind: CMB-only constraints versus CMB+DESI combinations. Within the [Formula: see text] model, decreasing [Formula: see text] shifts predictions toward the [Formula: see text] values preferred by the CMB+DESI combinations, but may yield too-large [Formula: see text]; we find [Formula: see text] provides a viable compromise region. For the [Formula: see text]-Starobinsky case, increasing [Formula: see text] raises [Formula: see text], but values [Formula: see text] generally exceed observational bounds on [Formula: see text]. The three decay channels modify the allowed ranges of [Formula: see text] and [Formula: see text], with the scalar channel giving the strongest restrictions. We conclude that both models remain consistent with current CMB-only data in restricted regions of parameter space, and that residual tension with the higher [Formula: see text] favored by CMB+DESI persists.