Can a variable gravitational constant resolve the Faint Young Sun Paradox ?

Abstract

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 ${\mathcal{L}}_{\odot }\propto G^7{M}_{\odot }^5$, the Sun's luminosity ${\mathcal{L}}_{\odot }$ 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 ${\mathcal{L}}_{\mathrm{SNIa}}\propto G^{-3/2}$, 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.

arXiv comment9 pages, 1 figure. Typo's corrected, acknowledgement added. Main results unchanged. Matches published version in IJMPD

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• Evolution of Size, Mass, and Density of Galaxies Since Cosmic Dawn
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