  The latest experimental results from the LHC and dark matter (DM) searches
suggest that the parameter space allowed in supersymmetric theories is subject
to strong reductions. These bounds are especially constraining for scenarios
entailing light DM particles. Previous studies have shown that light neutralino
DM in the Minimal Supersymmetric Standard Model (MSSM), with parameters defined
at the electroweak scale, is still viable when the low energy spectrum of the
model features light sleptons, in which case, the relic density constraint can
be fulfilled. In view of this, we have investigated the viability of light
neutralinos as DM candidates in the MSSM, with parameters defined at the grand
unification scale. We have analysed the optimal choices of non-universalities
in the soft supersymmetry-breaking parameters for both, gauginos and scalars,
in order to avoid the stringent experimental constraints. We show that light
neutralinos, with a mass as low as 25 GeV, are viable in supergravity scenarios
if the gaugino mass parameters at high energy are very non universal, while the
scalar masses can remain of the same order. These scenarios typically predict a
very small cross section of neutralinos off protons and neutrons, thereby being
very challenging for direct detection experiments. However, a potential
detection of smuons and selectrons at the LHC, together with a hypothetical
discovery of a gamma-ray signal from neutralino annihilations in dwarf
spheroidal galaxies could shed light on this kind of solutions. Finally, we
have investigated the naturalness of these scenarios, taking into account all
the potential sources of tuning. Besides the electroweak fine-tuning, we have
found that the tuning to reproduce the correct DM relic abundance and that to
match the measured Higgs mass can also be important when estimating the total
degree of naturalness.
