A Closer Earth and the Faint Young Sun Paradox: Modification of the Laws of Gravitation, or Sun/Earth Mass Losses?

Abstract

Given a solar luminosity L_Ar = 0.75 L_0 at the beginning of the Archean 3.8 Gyr ago, where L_0 is the present-day one, if the heliocentric distance r of the Earth was r_Ar = 0.956 r_0, the solar irradiance would have been as large as I_Ar = 0.82 I_0. It would allowed for a liquid ocean on the terrestrial surface which, otherwise, would have been frozen, contrary to the empirical evidence. By further assuming that some physical mechanism subsequently displaced the Earth towards its current distance in such a way that the irradiance stayed substantially constant over the entire Archean from 3.8 Gyr to 2.5 Gyr ago, a relative recession rate as large as \dot r/r \simeq 3.4 x 10^-11 yr^-1 would have been required. Although such a figure is roughly of the same order of magnitude of the value of the Hubble parameter 3.8 Gyr ago H_Ar = 1.192 H_0 = 8.2 x 10^-11 yr^-1, standard general relativity rules out cosmological explanations for the hypothesized Earth' s recession rate. Instead, a class of modified theories of gravitation with nonminimal coupling between the matter and the metric naturally predicts a secular variation of the relative distance of a localized two-body system, thus yielding a potentially viable candidate to explain the putative recession of the Earth' s orbit. Another competing mechanism of classical origin which could, in principle, allow for the desired effect is the mass loss which either the Sun or the Earth itself may have experienced during the Archean. On the one hand, this implies that our planet should have lost 2% of its present mass in the form of eroded/evaporated hydrosphere which, thus, should have been two orders of magnitude larger than now. On the other hand, it is widely believed that the Sun could have lost mass at an enhanced rate due to a stronger solar wind in the past for not more than \sim 0.2-0.3 Gyr.