Faint Young Sun, Planetary Paleoclimates and Varying Fundamental Constants

Abstract

The effect of a cosmic time variation of the gravitational constant on the solar luminosity evolution is studied. It is demonstrated that a varying gravitational constant can substantially affect the solar flux at the planetary orbits on geological time scales. Mean surface temperatures well above the freezing point of water can be achieved in this way throughout the Archean and Hadean, without invoking an increased greenhouse effect or a lower albedo. Instead of a monotonous decline of the solar flux in look-back time, due to a dim early Sun, we infer a flux minimum during the Early Proterozoic and Late Archean. In this epoch, the solar flux is capable of generating mean surface temperatures between 7 • C and 12 • C, as compared to the present 15 • C. The flux then steadily increases, culminating in temperatures between 12 • C and 19 • C some 4.5 Gry ago, depending on the parameters chosen for the 'standard' Sun. This explains the absence of polar caps, and even warm oceans in the Archean and Hadean are possible at these temperatures. No change of the present 33 K greenhouse effect is required. As for Mars, we show that the solar flux at the Martian orbit before 3.8 Gyr was at least 90% of the present-day flux, so that mean surface temperatures above the freezing point could have been generated by CO 2 greenhouse warming. The time variation of the gravitational constant is such that the moderate dimensionless ratio h 2 H 0 /(k 0 cm 3 π ) stays constant in cosmic time. There are stringent bounds on the logarithmic time derivative of the gravitational constant from lunar laser ranging and helioseismology, which indicate that the first-order derivative at the present epoch is too small to noticeably affect the solar luminosity evolution within the age of the Earth. However, higher-order derivatives have to be taken into account, as they do affect the solar flux in geologic look-back time. We consider the impact of a varying gravitational constant on the redshift scaling of the linear size of radio galaxies. The observed scaling exponent also enters the solar luminosity evolution. The age of the universe has a substantial imprint on planetary paleoclimates.

Redshift evolution of angular diameters and surface brightness: how rigid are galactic measuring rods?

“…Paleoclimatic estimates of planetary surface temperatures were used in Tomaschitz (2005) to single out the expansion factor defined by α = 1, β = −1/2, and η = 3/2, so that H 0 τ 0 ≈ 1.1572, cf. (2.3).…”

“…The expansion (3.5) applies to a hyperbolic 3-space; in the case of positive spatial curvature, we replaceR 2 by −R 2 . We turn to the high-z expansion of the metric distance D(z), and restrict the parameter range to 0 < α + β < 1, so that the integral in (3.1) stays finite for τ 1 → 0, as suggested by planetary paleoclimates (Tomaschitz 2005). Expanding (3.1) in ascending powers of τ 1 /τ 0 , and substituting the high-z expansion of…”

Effect of a varying gravitational constant on the SN Ia Hubble diagram, AGN luminosity evolution, and X-ray source counts

“…From now on, we restrict the parameter range to 0 < α + β < 1, so that the integral stays finite for τ 1 → 0, as suggested by planetary paleoclimates (Tomaschitz 2005). Expanding D(z) in ascending powers of τ 1 /τ 0 , we obtain…”

“…The context is an open Robertson-Walker cosmology with an expansion factor capable of explaining the "faint young sun paradox" (Newman and Rood 1977;Kasting and Catling 2003;Tomaschitz 2005) and resulting in a very small present-day variationḢ 0 /H 0 =Ġ 0 /G 0 ≈ 1.9×10 −4 Gyr −1 . The Hubble parameter is employed as universal scaling variable, determining the redshift evolution of the gravitational constant as well as of SN Ia and AGN luminosities.…”

“…Paleoclimatic estimates of planetary surface temperatures were used in Tomaschitz (2005) to single out the expansion factor defined by α = 1, β= −1/2, η= 3/2, (2.11) so that H 0 τ 0 ≈ 1.1572, see (2.8). This results in a cosmic age of τ 0 ≈ 16.635 Gyr and a deceleration parameter defined by ε ≈ −2.786×10 −3 , see (2.9), which determines the presentday logarithmic derivative,Ġ 0 /G 0 ≈ 1.938 × 10 −4 Gyr −1 , according to (2.5).…”