New generalization of the simplest <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>?</mml:mi></mml:mrow></mml:math> -attractor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi></mml:math> model

The simplest $\alpha$-attractor $T$ model is given by the potential $V=V_0\tanh^2(\lambda\phi/M_{pl})$. However its generalization to class of models type $V = V_0 \tanh^p (\lambda \phi/M_{pl})$ difficult interpret as a inflation for most values $p$. Keeping basic model, we propose new generalization, where final form (1-\sech^p \phi/M_{pl}))$, which does not present any problems that plague original allowing successful interpretation value $p$ and, at same time, providing with region reheating can occur (including odd and fractional values) without difficulty. In cases $p 1, 2, 4$ obtain solutions $r(n_s, N_{ke})$ $r$ tensor-to-scalar ratio, $n_s$ spectral index $N_{ke}$ number $e$-folds during inflation. We also show how these connect $\phi^2$ monomial.