Hubble and Cosmological Constants

[Enola Straight]

When Einstein was first formulating his General Theory of Relativity, he...as were all reputable scientists at time...assumed the universe was static and unchanging, and had to insert a Cosmological Constant to negate his mathematical model's tendency to expand over time.

Later, Astronomer Edwin Hubble discovered that distant galaxies are racing away from ours, indicating the universe was indeedexpanding...a discovery which made Einstein conclude his Cosmological Constant to be "the worst blunder of my life".

Lately, it has been found that the rate of universal expansion has not maintained a steady rate: ovewr the past 14 billion years, expansion has slowed down and sped up...indeed, we are now in an increasingly accelerating phase of universal expansion.

Does this imply the Hubble Constant is a function of the Cosmological Constant, or vice versa?

[Enola Straight]

Maybe if you express each in Planck Units?

[Kuroneko]

If the cosmological constant Λ is indeed a constant, then I'm not sure how to interpret your question meaningfully. If you mean whether in the various models of the big bang within GTR, the Hubble constant at some particular cosmological time has a dependency on Λ, then the answer is yes--along with density and spatial curvature (of hypersurface of homogeneity). According to MTW §29.1, H² = (8π/3)ρ - k/a² + Λ/3, where the first term is matter density (radiation density assumed to be too low to matter), the second is a spatial curvature term (a = scale factor), and the third is the cosmological constant.

On the other hand, for any particular universe, Λ would be fixed if GTR is correct. There are theories competing with GTR that can accommodate a time-varying Λ or even a varying gravitational constant G.