After Planck 2013, a broad class of inflationary models called $\alpha$-attractors was developed which has universal observational predictions. For small values of the parameter $\alpha$, the models have good consistency with the recent cosmic microwave background data. In this work, we first calculate analytically (and verify numerically) the predictions of these models for spectral index, $n_{\mathrm{s}}$, and tensor-to-scalar ratio, $r$, and then, using BICEP2/Keck 2015 and Planck 2015 data, we impose constraints on $\alpha$-attractors. Then, we study the reheating for $\alpha$-attractors. The reheating temperature, $T_{\mathrm{re}}$, and the number of e-folds during reheating, $N_{\mathrm{re}}$, are calculated as functions of $n_{\mathrm{s}}$. Using these results, we determine the range of the free parameters of two classes of $\alpha$-attractors which satisfy the constraints of recent cosmic microwave background data.

• Received 1 March 2016

DOI:https://doi.org/10.1103/PhysRevD.93.123517