  We explicitly compute the component action of certain recently discovered new
$\mathcal{N} = 1$ supergravity actions which enlarge the space of scalar
potentials allowed by supersymmetry and also contain fermionic interaction
terms that become singular when supersymmetry is unbroken. They are the
"Liberated Supergravity" introduced by Farakos, Kehagias and Riotto, and
supergravities with a new Kahler-invariant Fayet-Iliopoulos term proposed by
Antoniadis, Chatrabhuti, Isono, and Knoops. This paper is complementary to our
previous papers [Phys. Rev. D 103 (2021), 025008 and 105006], in which new
constraints on the coupling constants of those new theories were found. In this
paper we spell out many details that were left out of our previous papers.
