Undergrad What is the Hubble Parameter over time and how can I calculate it?

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The Hubble Parameter decreases over time and approaches a constant value, which can be calculated using the equation H∞=H0√ΩΛ, where ΩΛ represents the current dark energy density. Users can find graphical representations of this relationship through specific online calculators. The parameter's behavior indicates that as redshift (z) approaches -1, the Hubble Parameter stabilizes. Resources provided include a tutorial link for further understanding and a calculator for visualizing the data. Understanding the Hubble Parameter's evolution is crucial for cosmological studies.
Arman777
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How can I calculate the Hubble Parameter in time. I know that it decreases in time and approaches to some constant value but I am not sure to what value, Is there any graph for that ?
 
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Take a look at the first equation here:
https://www.physicsforums.com/insights/lightcone7-tutorial-part-iii-things-computed/
For far future, z tends to -1, so the equation reduces to ##H_\infty=H_0\sqrt{\Omega_\Lambda}## with current dark energy density as the input.
You can use the calculator itself to graph the relationship:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7-2017-02-08/LightCone_Ho7.html
upload_2019-1-30_8-46-35.png
 

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I always thought it was odd that we know dark energy expands our universe, and that we know it has been increasing over time, yet no one ever expressed a "true" size of the universe (not "observable" universe, the ENTIRE universe) by just reversing the process of expansion based on our understanding of its rate through history, to the point where everything would've been in an extremely small region. The more I've looked into it recently, I've come to find that it is due to that "inflation"...

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