  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.
