The geoid low over French Polynesia has been previously interpreted as the signature of an upper mantle upwelling associated with a low-viscosity zone located immediately below the lithosphere. We propose here an alternative explanation using new high-quality satellite gravity data and fluid mechanics constraints. We thus discuss the origin of the high concentration of hotspots in the Central Pacific, which is still debated. Satellite gravity data from the GRACE mission analyzed with wavelets allow us to better characterize the geoid low on French Polynesia and the large-scale positive geoid anomaly 600 km east of the Line Islands chain. We show that the geoid anomalies are consistent with thermochemical oscillating domes and we bring constraints on their density contrast and their upper limit depth under this hypothesis. The Central Pacific mantle would contain two thermochemical instabilities at different stages of their development: a rising dome (lighter) extending approximately from the CMB up to the transition zone beneath the South Pacific Superswell, toped by secondary plumes that generate short-lived hot spot chains, and a sinking dome (denser) in the lower mantle beneath the area located 600 km east of the Line Islands chain. Plate reconstructions further show that the latter could also have generated the Southern Line Islands 35 M.y. ago and Shatsky Rise 140 M.y. ago when it was in its ascending phase, while the South Pacific dome probably created Darwin Rise 100 M.y. ago in a same type of event.