Can a variable gravitational constant resolve the faint young Sun paradox?

Solar models suggest that four billion years ago the young Sun was similar to 25% fainter than it is today, rendering Earth's oceans frozen and lifeless. However, there is ample geophysical evidence that Earth had a liquid ocean teeming with life 4 Gyr ago. Since L circle dot proportional to (CM circle dot 5)-M-7, the Sun's luminosity L-circle dot is exceedingly sensitive to small changes in the gravitational constant G. We show that a percent-level increase in G in the past would have prevented Earth's oceans from freezing, resolving the faint young Sun paradox. Such small changes in G are consistent with observational bounds on Delta G/G. Since L-SNIa proportional to G(-3/2), an increase in G leads to fainter supernovae, creating tension between standard candle and standard ruler probes of dark energy. Precisely such a tension has recently been reported by the Planck team.