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.
Categories: astro-ph.SR astro-ph.CO astro-ph.EP gr-qc hep-ph