  Supergravity embedding of the Standard Model of particle physics provides
phenomenologically well-motivated and observationally viable inflationary
scenarios. We investigate a class of inflationary models based on the
superconformal framework of supergravity and discuss constraints from the
reheating temperature, with the particular focus on the gravitino problem
inherent in these scenarios. We point out that a large part of the parameter
space within the latest BICEP/Keck 95\% confidence contour may have been
excluded by the gravitino constraints, depending on the mass scale of the
inflaton. Precision measurements of the scalar spectral index by a future
mission may rule out some of these scenarios conclusively.
