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We study the supersymmetric extension of $SO(10)$-inspired thermalleptogenesis showing the constraints on neutrino parameters and on the reheattemperature $T_{\rm RH}$ that derive from the condition of successfulleptogenesis from next-to-lightest right handed (RH) neutrinos ($N_2$) decaysand the more stringent ones when independence of the initial conditions (strongthermal leptogenesis) is superimposed. In the latter case, the increase of thelightest right-handed neutrino ($N_1$) decay parameters helps the wash-out of apre-existing asymmetry and constraints relax compared to the non-supersymmetriccase. We find significant changes especially in the case of large $\tan\beta$values $(\gtrsim 15)$. In particular, for normal ordering, the atmosphericmixing angle can now be also maximal. The lightest (ordinary) neutrino mass isstill constrained within the range $10 \lesssim m_1/{\rm meV} \lesssim 30$(corresponding to $75\lesssim \sum_i m_i/{\rm meV} \lesssim 120$). Invertedordering is still disfavoured, but an allowed region satisfying strong thermalleptogenesis opens up at large $\tan\beta$ values. We also study in detail thelower bound on $T_{\rm RH}$ finding $T_{\rm RH}\gtrsim 1 \times 10^{10}\,{\rmGeV}$ independently of the initial $N_2$ abundance. Finally, we propose a new$N_2$-dominated scenario where the $N_1$ mass is lower than the sphaleronfreeze-out temperature. In this case there is no $N_1$ wash-out and we find$T_{\rm RH} \gtrsim 1\times 10^{9}\,{\rm GeV}$. These results indicate that$SO(10)$-inspired thermal leptogenesis can be made compatible with the upperbound from the gravitino problem, an important result in light of the roleoften played by supersymmetry in the quest of a realistic model of fermionmasses.

Supersymmetric $SO(10)$-inspired leptogenesis and a new $N_2$-dominated scenario