The detection of the signature of dipole gravity modes has opened the path to study the solar inner radiative zone. Indeed, g modes should be the best probes to infer the properties of the solar nuclear core that represents more than half of the total mass of the Sun. Concerning the dynamics of the solar core, we can study how future observations of individual g modes could enhance our knowledge of the rotation profile of the deep radiative zone. Applying inversions on a set of real p-mode splittings coupled with either one or several g modes, we have checked the improvement of the inferred rotation profile when different error bars are considered for the g modes. Moreover, using a new methodology based on the analysis of the almost constant separation of the dipole gravity modes, we can introduce new constraints on solar models. For that purpose, we can compare g-mode predictions computed from several models including different physical inputs with the g-mode asymptotic signature detected in Global Oscillations at Low Frequencies (GOLF) data and calculate the correlation. This work shows the great consistency between the signature of dipole gravity modes and our knowledge of p-modes: incompatibility of data with a present standard model including the Asplund composition.