  Solar models suggest that four billion years ago the young Sun was about 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 ${\cal L_\odot} \propto G^7M_\odot^5$, the
Sun's luminosity ${\cal L_\odot}$ 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 ${\cal L}_{\rm SNIa} \propto G^{-3/2}$, 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.
