Generalized dilaton-axion models of inflation, de Sitter vacua and spontaneous SUSY breaking in supergravity

We propose the unified models of cosmological inflation, spontaneous SUSY breaking, and the dark energy (de Sitter vacuum) in $N=1$ supergravity with the dilaton-axion chiral superfield $T$ in the presence of an $N=1$ vector multiplet with the alternative Fayet-Iliopoulos term. By using the K"ahler potential as $K=-\alpha \log (T+\bar{T})$ and the superpotential as a sum of a constant and a linear term, we find that viable inflation is possible for $3\le \alpha \le {\alpha }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ where ${\alpha }_{\mathrm{m}\mathrm{a}\mathrm{x}}\approx 7.235$. Observations of the amplitude of primordial scalar perturbations fix the SUSY breaking scale in our models as high as ${10}^{13}$ GeV. In the case of $\alpha >3$ the axion gets the tree-level (non-tachyonic) mass comparable to the inflaton mass.