  The generalized Einstein Hilbert action is an extension of the classic scalar
curvature energy and Perelman F functional which incorporates a closed
three-form. The critical points are known as generalized Ricci solitons, which
arise naturally in mathematical physics, complex geometry, and generalized
geometry. Through a delicate analysis of the group of generalized gauge
transformations, and implementing a novel connection, we give a simple formula
for the second variation of this energy which generalizes the Lichnerowicz
operator in the Einstein case. As an application, we show that all Bismut flat
manifolds are linearly stable critical points, and admit nontrivial
deformations arising from Lie theory. Furthermore, this leads to extensions of
classic results of Koiso and Podesta, Spiro, Kr\"oncke to the moduli space of
generalized Ricci solitons. To finish we classify deformations of the
Bismut-flat structure on S3 and show that some are integrable while others are
not.
