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

TL;DR

This study probes the existence and magnitude of local Hubble expansion within the Solar System by linking planetary thermal histories to cosmological evolution. It develops a universal heat-balance model in which planetary surface temperature evolves with solar luminosity and the cosmological scale factor via $T_s(t)/T_{s0} = [L(t)/L_0]^{1/4} [a(t)/a_0]^{-1/2}$, with $L(t) = L_0 (1 - \frac{2}{5} t/t_S)^{-1}$ and $a'(\tau) = a \sqrt{(1-\Omega_{D0}) + \Omega_{D0}(a_0/a)^3}$ under a flat $\Lambda$CDM background. Using Earth and Mars paleotemperature proxies (isotopic, biological, and oceanic records) and Precambrian constraints, the authors infer local $H_0$ values that range from roughly $70$–$150$ km s$^{-1}$ Mpc$^{-1}$ depending on epoch and cosmological model, with Precambrian data favoring closer to the global $H_0$ (≈70 km s$^{-1}$ Mpc$^{-1}$). These results align qualitatively with Earth–Moon tidal estimates, but large geophysical uncertainties limit decisiveness; the work emphasizes the potential to test cosmology within the Solar System, while acknowledging the need for refined data and modeling. Overall, the paper highlights that local cosmological effects may be detectable through planetary histories, offering a cross-check against intergalactic measurements and inviting further interdisciplinary investigation.

Abstract

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 the 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 standard LambdaCDM model with 70% of dark energy, contemporary value of the local Hubble parameter was found to be 70-90 km/s/Mpc under assumption that the Earth's surface temperature in the end of Precambrian equaled 45 C. This 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.

Figures (2)

• Figure 1: Observational data on the relative surface temperatures of the Earth and Mars $T_{\rm s}/T_{\rm s0}$ (upper left panel) vs. the theoretical predictions by a few cosmological models at various values of the Hubble parameter normalized to $h = 100$ km/s/Mpc (dotted curves in three other panels). Solid curves correspond to the standard intergalactic value of the Hubble parameter; and the long-dashed curves, to the original Křı́žek--Somer model Krizek_12Krizek_15.
• Figure 2: Observational data on the relative surface temperature of the Earth $T_{\rm s}/T_{\rm s1}$vs. the theoretical predictions by the standard cosmological model (${\Omega}_{\Lambda} = 0.7$, ${\Omega}_{\rm D} = 0.3$) for three different temperatures in the end of Precambrian $T_{\rm s1}$. All designations are the same as in Fig. \ref{['fig:T-t']}, and the temporal period excluded from the analysis is shaded in gray.