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 $\alpha$.