Subtle oscillation of G over time
v. 7 n. 17
The gravitational constant, G, is conventionally considered exclusively a measured value,
G = 6.67430 x 10^-11 m^3 kg^-1 s^-2.
The theoretical (late-time) approximation from these Letters based on measured parameters in Equation (1) is
G = G_0 ≈ 6.46 x 10^-11 m^3 kg^-1 s^-2;
this value serves as reference points on the graph in the cover image. It occurs three times -- once in each era, indicating the stability of the gravitational constant, regardless of the freedom given it in the theoretical relation used to plot the curve in this image,
G = (3H^2 + 3 a2 /a) / 8πρ. ....................................... (1)
This relation is derived and explained in the previous Letter, where measured values for the parameters at late-time are indicated. * The parameters on the right vary considerably over the cosmic eras, yet the value of G is stable, and consistent with conventional expectations in each era. This suggests that other natural constants may be similarly relational rather than intrinsic.
In terms of redshift, z, and time, the boundaries between eras in this log scale occur at
z ≈ 3400 for radiation-matter boundary; roughly 30,000 years after the beginning,
z ≈ 0.3 for matter-late time boundary; 3.3 billion years after the beginning,
z = 0 for the present (G = 6.46 x 10^-11); 13.8 billion years after the beginning.
A slight decline in G is projected in the future, consistent with the past mild oscillation.
The measured value of G may be used to recalibrate the vertical axis, so that the graph with additional data points might be used to recalculate the measured parameters for the late-time, either to refine the measured values or serve as theoretical predictions to confirm or falsify theory.