Estimating the Local Hubble Parameter from the Thermal Evolution of Earth and Mars

The problem of local (e.g., interplanetary) Hubble expansion is studied for a long time but remains a controversial subject till now; and of particular interest is a plausible value of the local Hubble parameter at the scale of the Solar system. Here, we tried to estimate the corresponding quantity by the analysis of surface temperatures on the Earth and Mars, which are formed by a competition between a variable luminosity of the Sun and increasing radii of the planetary orbits. Our work employs paleochemical and paleobiological data on the temperature of the ancient Earth, on the one hand, and geological data on the existence of an ocean of liquid water on the ancient Mars, on the other hand. As follows from our analysis, the martian data impose only a weak constraint on the admissible values of the Hubble parameter because of unknown salinity, and therefore the freezing point of the martian water. On the other hand, the terrestrial data turn out to be much more valuable, especially, for the Precambrian period, when temperature variation was sufficiently smooth and monotonic. For example, in the framework of the standard $$\Lambda$$ CDM model with 70 $$\%$$ of dark energy, the contemporary value of the local Hubble parameter was found to be 70–90 km/s/Mpc under assumption that the Earth’s surface temperature at the end of Precambrian equaled $$45^{\circ}$$ C. It is in reasonable agreement both with the intergalactic data and with an independent estimate of the local Hubble parameter from tidal evolution of the Earth–Moon system.