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

TL;DR

This paper proposes that a slight increase in the gravitational constant in Earth's past could explain the Faint Young Sun Paradox by maintaining sufficient solar luminosity for liquid oceans, aligning with observational bounds.

Contribution

It introduces the idea that small historical variations in G can resolve the paradox and links this to tensions in dark energy measurements from supernovae and cosmological data.

Findings

A percent-level increase in G would have kept Earth's oceans liquid 4 Gyr ago.

Such variations in G are consistent with current observational constraints.

An increased G would result in fainter supernovae, explaining recent tensions in dark energy measurements.

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 ${\cal L_\odot} \propto G^7M_\odot^5$, 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.