Faint young sun paradox
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The faint young sun paradox describes the apparent contradiction between observations of liquid water early in Earth's history and the astrophysical expectation that the sun's output would be only 70% as intense during that epoch as it is during the modern epoch.
The standard solar model describes the history and evolution of stars. An aspect of this model is that stars similar to the sun should gradually brighten over their life time (excluding a very bright phase just after formation). This prediction is supported by the observation of lower brightness in young stars of solar type. However, with the predicted brightness 4 billion (109) years ago and with greenhouse gas concentrations the same as are current for the modern Earth, any liquid water exposed to the surface would quickly freeze solid. This contradicts geological observations of sedimentary rocks, which required the presence of flowing liquid water to form.
The tension between the two hypothesis stems from the incorrect assumption that atmospheric gas concentrations in the past were the same as today. First, before the advent of abundant life the atmospheric oxygen concentrations were orders of magnitude lower than today. In the presence of oxygen methane breaks down to carbon dioxide, so in the absence of oxygen the methane concentration could be much larger than currently observed. Methane is a more potent greenhouse gas than carbon dioxide, so the relative abundance of atmospheric methane throughout Earth's history must be considered when modeling the temperature.
Further, the inorganic version of the carbon cycle can be expected to provide negative feedback towards an Earth with liquid water. Carbon dissolved in liquid water can form carbonic acids, which can then interact with calcium to produce calcium carbonate. If rainfall were to cease and the oceans froze over, then this part of the inorganic carbon cycle would shut down. Periodic explosions from volcanoes would then cause a net increase in the atmospheric carbon dioxide and methane levels with no liquid water to absorb these emitted gases. Eventually the concentrations would become large enough that the surface temperature would rise due to the greenhouse effect. When the surface temperature became large enough for the oceans to melt and rainfall to resume the other half of the inorganic carbon cycle would turn on and moderate the greenhouse gas concentrations.
It is also noteworthy, that even though evidence of flowing water exists even from very early in Earth's history, there may still have been a number of examples of periods when the Earth's oceans froze over completely. It is hypothesized that the most recent such period may have been ~630 million years ago, and may have been instrumental in leading the Cambrian explosion of new multicellular life forms.
