Faint Young Sun,Planetary Paleoclimates and Varying Fundamental Constants

The effect of a cosmic time variation of the gravitational constant on the solar luminosity evolution is studied. It is demonstrated that a varying gravitational constant can substantially affect the solar flux at the planetary orbits on geological time scales. Mean surface temperatures well above the freezing point of water can be achieved in this way throughout the Archean and Hadean, without invoking an increased greenhouse effect or a lower albedo. Instead of a monotonous decline of the solar flux in look-back time, due to a dim early Sun, we infer a flux minimum during the Early Proterozoic and Late Archean. In this epoch, the solar flux is capable of generating mean surface temperatures between 7^∘C and 12^∘C, as compared to the present 15^∘C. The flux then steadily increases, culminating in temperatures between 12^∘C and 19^∘C some 4.5 Gry ago, depending on the parameters chosen for the ‘standard’ Sun. This explains the absence of polar caps, and even warm oceans in the Archean and Hadean are possible at these temperatures. No change of the present 33 K greenhouse effect is required. As for Mars, we show that the solar flux at the Martian orbit before 3.8 Gyr was at least 90% of the present-day flux, so that mean surface temperatures above the freezing point could have been generated by CO₂ greenhouse warming. The time variation of the gravitational constant is such that the moderate dimensionless ratio ħ² H₀/(k₀ cm_π³) stays constant in cosmic time. There are stringent bounds on the logarithmic time derivative of the gravitational constant from lunar laser ranging and helioseismology, which indicate that the first-order derivative at the present epoch is too small to noticeably affect the solar luminosity evolution within the age of the Earth. However, higher-order derivatives have to be taken into account, as they do affect the solar flux in geologic look-back time. We consider the impact of a varying gravitational constant on the redshift scaling of the linear size of radio galaxies. The observed scaling exponent also enters the solar luminosity evolution. The age of the universe has a substantial imprint on planetary paleoclimates.