  The dynamics of the solar core cannot be properly constrained through the
analysis of acoustic oscillation modes. Gravity modes are necessary to
understand the structure and dynamics of the deepest layers of the Sun. Through
recent progresses on the observation of these modes -- both individually and
collectively -- new information could be available to contribute to inferring
the rotation profile down inside the nuclear burning core. To see the
sensitivity of gravity modes to the rotation of the solar core. We analyze the
influence of adding the splitting of one and several g modes to the data sets
used in helioseismic numerical inversions. We look for constraints on the
uncertainties required in the observations in order to improve the derived core
rotation profile. We compute forward problems obtaining three artificial sets
of splittings derived for three rotation profiles: a rigid profile taken as a
reference, a step-like and a smoother profiles with higher rates in the core.
We compute inversions based on Regularized Least-Squares methodology (RLS) for
both artificial data with real error bars and real data. Several sets of data
are used: first we invert only p modes, then we add one and several g modes to
which different values of observational uncertainties (75 and 7.5 nHz) are
attributed. For the real data, we include g-mode candidate, l=2, n=-3 with
several splittings and associated uncertainties. We show that the introduction
of one g mode in artificial data improves the rate in the solar core and give
an idea on the tendency of the rotation profile. The addition of more g modes
gives more accuracy to the inversions and stabilize them. The inversion of real
data with the g-mode candidate gives a rotation profile that remains unchanged
down to 0.2 R, whatever value of splitting we attribute to the g mode.
