7 keV Sterile neutrino dark matter in $U(1)_R-$ lepton number model
  We study the phenomenology of a keV sterile neutrino in a supersymmetric
model with $U(1)_R-$ lepton number in the light of a very recent observation of
an X-ray line signal at around 3.5 keV, detected in the X-ray spectra of
Andromeda galaxy and various galaxy clusters including the Perseus galaxy
cluster. This model not only provides a small tree level mass to one of the
active neutrinos but also renders a suitable warm dark matter candidate in the
form of a sterile neutrino with negligible active-sterile mixing. Light
neutrino masses and mixing can be explained once one-loop radiative corrections
are taken into account. The scalar sector of this model can accommodate a Higgs
boson with a mass of $\sim$ 125 GeV. In this model gravitino is the lightest
supersymmetric particle (LSP) and we also study the cosmological implications
of this light gravitino with mass $\sim \mathcal O$(GeV).
