Aspects of supersymmetry breaking driven inflation in orbifold models

We consider gravitationally induced corrections to inflaton potentials driven by supersymmetry breaking in a five-dimensional supergravity, compactified on a $S_1/Z_2$ orbifold. The supersymmetry breaking takes place on the hidden brane and is transmitted to the visible brane through finite one loop graphs giving rise to an inflaton potential which includes gravitationally induced terms. These corrections are significant for inflationary cosmology and have the potential to modify the predictions of widely studied supergravity models if the latter are embedded in this framework. To explore these effects we examine two classes of models those inspired by no-scale supergravity models and $\alpha$-attractors. Both models are compatible with current cosmological observations but face chalenges in reconciling enhanced values for the scalar power spectrum $P_\zeta$ with cosmological data, particularly regarding the tensor to scalar ratio $r$. In fact $P_\zeta \gtrsim 10^{-2}$ results to $r > \mathcal{O} (0.1)$, outside the limits put by current data.