$\alpha$-attractor from superconformal E-models in brane inflation.

In the large extra dimensional braneworld inflation, Friedmann equation is modified to include a quadratic term in energy density with an additional parameter $\lambda$ called brane tension in addition to the usual linear term. The high energy brane corrections modify the slow-roll parameters and affect the behaviour of inflation. We analyse the superconformal inflation for E-models and find that there exist $\alpha$-attractors in brane inflation. The predictions for the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ are computed numerically, and approximate analytic formulas in the high energy limit have been given for the observable $n_s$ and $r$. The constraints on the model parameters are obtained by using Planck 2018 and BICEP2 observational data.