Constraining $\alpha$-attractor models from reheating

Understand

We eliminate the parameters originally present in models of inflation of the $\alpha$-attractor type in favor of the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$.

• We then write expressions for the number of $e$-folds during reheating $ N_ {re} $.
• By imposing reasonable conditions on $N_{re}$ we can restrict $n_s$ and $r$ and in turn, we use these constraints in order to find bounds for cosmological quantities of interest such as the number of $e$-folds during inflation and the radiation dominated eras, as well as for the reheating temperature and the running index.
• The minimum condition that $N_ {re}$ must satisfy is $N_ {re}\geq 0$ which we use to constrain the cosmological quantities mentioned above.