Gravity modes are the best probes to study the solar radiative zone dynamics, especially in the nuclear core. These modes remain difficult to observe, but they are essential ingredients for progressing on the evolution of the Sun-Earth relationship at the level of centuries. Today, the knowledge of the internal dynamics comes from acoustic modes and concerns mainly the external 2% of the solar mass. Nevertheless, the flat rotation profile of the radiative zone compels physics beyond the standard framework. I summarize different attempts to look for gravity modes and the results obtained after 8 years of observation with the GOLF/SoHO instrument. Some gravity mode candidates (at 1mm/s level) have appeared with more than 98% confidence level as quadruplets or quintuplets. These patterns, if confirmed as gravity modes, may reveal very exciting physics of the solar core. Getting information on rotation and magnetic field in the solar core are real keys to simulate a complete dynamical solar picture. The understanding of the solar dynamics, the precise energetic balance and its temporal evolution necessitate more observations of the radiative zone which constitutes 98% of the Sun by mass. Our expertise in Doppler velocity measurements allows a step further and a new instrumental concept to reach velocities as low as 0.1 mm/s. A prototype will join the Tenerife site in 2006 and a space version is proposed to CNES and ESA as a microsatellite or part of a payload at the L1 Lagrange point.
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