Hubble Constant, Dark Energy and the Expanding Universe

[PhanthomJay]

TL;DR Summary

Recent info from Hubble suggests an Increasing Hubble constant (Source: NASA) that was originally thought to be decreasing, especially since Dark Energy assists in decreasing the expansion due to its own accelerating expansion properties that are making the universe less dense. Please explain this paradox.

Why was the Hubble constant assumed to be decreasing and slowing down (decelerating) the expansion rate of the Universe, while at the same time Dark Energy is presumably accelerating the expansion? And to thicken the plot. recent news from NASA indicates that the Hubble constant is now increasing. Can you clarify this enigma? Also., if the Hubble constant eventually decreases, why is there a lower limit to its value?

 

[Hill]

I think about it as follows:
The Hubble parameter $H=\frac {\dot a} a$, where $a$ is the scale factor. To see how it changes in time, I take $\dot H=\frac {\ddot a a-\dot a \dot a}{a^2}$.
If the expansion is constant, $\ddot a =0$, then $\dot H \lt 0$, i.e., the Hubble parameter decreases.
If the expansion accelerates, $\ddot a \gt 0$, then the Hubble constant increases if $\ddot a a \gt {\dot a}^2$ and decreases otherwise. So, the outcome depends on the values of $a, \dot a,$ and $\ddot a$ at the moment.

 

[Orodruin]

This is a common confusion. The bottom line is that when we say accelerating expansion we mean $\ddot a > 0$, which means that $\dot a$ increases, whereas the Hubble parameter is $\dot a/ a$. Even if $\dot a$ increases, $H$ might not as covered in the previous post. In fact, in a dark energy dominated universe, $H$ is constant.