Ocean planets are volatile-rich planets, not present in our Solar system, which are thought to be dominated by deep, global oceans. This results in the formation of high-pressure water ice, separating the planetary crust from the liquid ocean and, thus, also from the atmosphere. Therefore, instead of a carbonate-silicate cycle like on the Earth, the atmospheric carbon dioxide concentration is governed by the capability of the ocean to dissolve carbon dioxide (CO2). In our study, we focus on the CO2 cycle between the atmosphere and the ocean which determines the atmospheric CO2 content. The atmospheric amount of CO2 is a fundamental quantity for assessing the potential habitability of the planet's surface because of its strong greenhouse effect, which determines the planetary surface temperature to a large degree. In contrast to the stabilizing carbonate-silicate cycle regulating the long-term CO2 inventory of the Earth atmosphere, we find that the CO2 cycle feedback on ocean planets is negative and has strong destabilizing effects on the planetary climate. By using a chemistry model for oceanic CO2 dissolution and an atmospheric model for exoplanets, we show that the CO2 feedback cycle can severely limit the extension of the habitable zone for ocean planets.Read less <