Testing $\alpha$-attractor P-model of inflation by Cosmic Microwave Background radiation

In a recently proposed approach to testing models of inflation by Cosmic Microwave Background (CMB) radiation the reheating temperature is directly expressed in terms of the CMB observables. Its model independent bounds translate in a given model into narrow ranges of those observables. In that approach we analyse the polynomial class of the $\alpha$-attractor inflaton potential models (P-models), in a broad range of polynomials and with the inflaton decays and fragmentation in the reheating period taken into account. The predictions for the CMB observables, the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$, are compared with the Planck and Planck combined with ACT data. Both can be accommodated by that class of the $\alpha$ attractor models. The sensitivity of the results of that comparison to the reheating temperature and to the upper bound on the ratio $r$ is clearly demonstrated.