Dilaton-Axion Inflation with PBHs and GWs
  We discuss two-stage dilaton-axion inflation models [1] and describe
$\alpha$-attractor models with either exponential or polynomial approach to the
plateau. We implement one of the models of primordial black hole production
proposed in [2] in the $\alpha$-attractor context, and develop its supergravity
version. The predictions of this model following from its polynomial attractor
properties are: $n_s$ and $r$ are $\alpha$-independent, $r$ depends on the mass
parameter $\mu$ defining the approach to the plateau. The tachyonic instability
at the transition point between the two stages of inflation is proportional to
the negative curvature of the hyperbolic space $\mathcal{R}_K=-2/3\alpha$.
Therefore the masses of primordial black holes (PBHs) and the frequencies of
small-scale gravitational waves (GWs) in this model show significant dependence
on $\alpha$.
