a-cosmology-group/acg#234

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#234 Hubble's parameter vs Hubble's constant
mikehellandmikehelland, edited OpenCosmology Models/Derivations

This applies to FLRW models, which LCDM is based on.

FLRW models have a Hubble parameter, $H$, and a Hubble constant, $H_0$, related by this:

$$H = H_0 [\Omega_M (1+z)^3 + \Omega_\Lambda]^{1/2}$$

Hubble’s constant, $H_0$ is the expansion rate today.

In a de Sitter model, aka pure dark energy, aka exponentially expanding model you have:

$$\Omega_M = 0.0$$

$$\Omega_\Lambda = 1.0$$

$$[\Omega_M (1+z)^3 + \Omega_\Lambda] = 1$$

$$H = H_0$$

The expansion rate never changes.

In LCDM you have:

$$\Omega_M = 0.3$$

$$\Omega_\Lambda = 0.7$$

Which gives us something like this:

image

It was larger in the past, and is settles on a value around 55 in the infinite future.

You can use this to try your own parameters:

https://mikehelland.github.io/hubbles-law/other/expansionrate/expansionrate.htm

To try to address a question by @ExpEarth, you can play with the parameters like this:

$$\Omega_M = -0.1$$

$$\Omega_\Lambda = 1.1$$

And the Hubble parameter will be lower in the past, rather than higher. I tried to compute luminosity distances that model, but it started complaining about not real numbers.

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Comments (1)

As is explained in the section Hubble Parameter at my website, the favorite model associated with the Variable Mass Theory is a de Sitter like cosmological model with accompanying constant Hubble parameter and an ( equivalent ) exponential expansion rate that never changes. A non-empty universe, filled with common mass and without dark energy.

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