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Given a solar luminosity L_Ar = 0.75 L_0 at the beginning of the Archean 3.8Gyr ago, where L_0 is the present-day one, if the heliocentric distance r ofthe Earth was r_Ar = 0.956 r_0, the solar irradiance would have been as largeas I_Ar = 0.82 I_0. It would allowed for a liquid ocean on the terrestrialsurface which, otherwise, would have been frozen, contrary to the empiricalevidence. By further assuming that some physical mechanism subsequentlydisplaced the Earth towards its current distance in such a way that theirradiance stayed substantially constant over the entire Archean from 3.8 Gyrto 2.5 Gyr ago, a relative recession rate as large as \dot r/r \simeq 3.4 x10^-11 yr^-1 would have been required. Although such a figure is roughly of thesame 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 outcosmological explanations for the hypothesized Earth' s recession rate.Instead, a class of modified theories of gravitation with nonminimal couplingbetween the matter and the metric naturally predicts a secular variation of therelative distance of a localized two-body system, thus yielding a potentiallyviable 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 Earthitself may have experienced during the Archean. On the one hand, this impliesthat our planet should have lost 2% of its present mass in the form oferoded/evaporated hydrosphere which, thus, should have been two orders ofmagnitude larger than now. On the other hand, it is widely believed that theSun could have lost mass at an enhanced rate due to a stronger solar wind inthe past for not more than \sim 0.2-0.3 Gyr.

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