  It is shown that in the phenomenologically realistic supersymmetric $B-L$
MSSM theory, a linear combination of the neutral, up Higgs field with the third
family left-and right-handed sneutrinos can play the role of the cosmological
inflaton. Assuming that supersymmetry is softly broken at a mass scale of order
$10^{13}~\mathrm{GeV}$, the potential energy associated with this field allows
for 60 e-foldings of inflation with the cosmological parameters being
consistent with all Planck2015 data. The theory does not require any
non-standard coupling to gravity and the physical fields are all sub-Planckian
during the inflationary epoch. It will be shown that there is a "robust" set of
initial conditions which, in addition to satisfying the Planck data,
simultaneously are consistent with all present LHC phenomenological
requirements.
