I 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.

 

[Jaime Rudas]

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.

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.

As @Hill rightly points out, if the expansion accelerates, the Hubble parameter $H$ could theoretically increase, remain constant, or decrease. In the most plausible current model (a dark energy dominated universe), $H$ decreases. In the de Sitter universe, whose only component is the cosmological constant $\Lambda$, $H$ is constant.

 

[ohwilleke]

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?

While not answering your technical question about the functional relationship of the different constants (others have already addressed that), the reason that this is coming up at all is because improved astronomy suggests that the Hubble constant may not be constant.

The possibility that Hubble's constant was changing over time was something that was hinted at by the Hubble Space Telescope, which further astronomy observations in the last five years or so have reinforced. (Another thread in the cosmology forum with 94 posts so far reviews how strong the evidence for that hypothesis is, which is a matter of ongoing debate among astrophysicists.)

The measured value of Hubble's constant in the later universe is consistently higher than its measured value at the time of that the Cosmic Microwave Background was formed, and we're not sure why this is the case.

The indications that it has changed over time were heightened by recent observations that are more fine grained over multiple time periods in the history of the universe from the Dark Energy Spectroscopic Instrument (DESI) observatory, in Arizona. These observations prefer a non-constant Hubble constant and as a consequence, non-constant (a.k.a. dynamic) dark energy.

 

[Jaime Rudas]

TL;DR Summary: Recent info from Hubble suggests an Increasing Hubble constant (Source: NASA) that was originally thought to be decreasing,

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.

... improved astronomy suggests that the Hubble constant may not be constant.

The possibility that Hubble's constant was changing over time was something that was hinted at by the Hubble Space Telescope,

The measured value of Hubble's constant in the later universe is consistently higher than its measured value at the time of that the Cosmic Microwave Background was formed, and we're not sure why this is the case.

The indications that it has changed over time were heightened by recent observations that are more fine grained over multiple time periods in the history of the universe from the Dark Energy Spectroscopic Instrument (DESI) observatory, in Arizona. These observations prefer a non-constant Hubble constant and as a consequence, non-constant (a.k.a. dynamic) dark energy.

I think four concepts are being mixed up here that, although related, are very different: the Hubble parameter, the Hubble constant, the expansion rate, and the cosmological constant.

The Hubble parameter tells us the speed of galaxies' recession as a function of their distance. This parameter is constant in space, but varies over time. In the most widely accepted cosmological model, this parameter is constantly decreasing.

The Hubble constant is the current Hubble parameter.

The expansion rate refers to the rate of increase (or decrease) of the scale factor.

The cosmological constant is the factor that explains the acceleration of the expansion, that is, the acceleration of the growth of the scale factor.

 

[Bandersnatch]

The possibility that Hubble's constant was changing over time was something that was hinted at by the Hubble Space Telescope, which further astronomy observations in the last five years or so have reinforced. (Another thread in the cosmology forum with 94 posts so far reviews how strong the evidence for that hypothesis is, which is a matter of ongoing debate among astrophysicists.)

The measured value of Hubble's constant in the later universe is consistently higher than its measured value at the time of that the Cosmic Microwave Background was formed, and we're not sure why this is the case.

The indications that it has changed over time were heightened by recent observations that are more fine grained over multiple time periods in the history of the universe from the Dark Energy Spectroscopic Instrument (DESI) observatory, in Arizona. These observations prefer a non-constant Hubble constant and as a consequence, non-constant (a.k.a. dynamic) dark energy.

1. this is an old thread - I'm not sure it's worth trying to engage with posts from close to two years back. Shame on Jamie for resurrecting the thread for no good reason.
2. I'm surprised that you'd misinterpret this so, given the general quality of your posting history, or the earlier posts in this thread providing clarification. Maybe it's me who's misreading your intent.
After all, the H0 doesn't change by definition, while that the Hubble parameter has to be changing must have been obvious ever since Hubble's observations were married to the framework of the FLRW metric. It decreasing with time is a necessary feature of any universe that's not fully dominated by dark energy. This is what the 'technical' posts you referred to explained.
Non-constant H hardly implies dynamic dark energy - although increasing, or not sufficiently decreasing, H could.
Furthermore, this is rather tangential to the Hubble tension issue, which btw doesn't measure a higher value of H at the present time than at recombination - the value at recombination was way, way higher. It's the present-time value extrapolated from the conditions in the past that doesn't quite measure up to the value for the same cosmic time, only measured more directly. Even assuming that this is a physics issue and not a measurement one, it isn't showing increasing H0. At best, it'd be showing an H that is not decreasing sufficiently fast, which could be due to growing dark energy density. Perhaps that's what you wanted to say.

 

[fresh_42]

Shame on Jamie for resurrecting the thread for no good reason.

I appreciated his clarification and, in particular, the clear list of the different terms in one short post. So after all, it added value to the thread, even if old.

 

[Jaime Rudas]

1. this is an old thread - I'm not sure it's worth trying to engage with posts from close to two years back. Shame on Jamie for resurrecting the thread for no good reason.

The reason I decided to revive this thread is because I noticed that the final conclusion ("in a dark energy dominated universe, $H$ is constant") seemed incorrect to me, and I considered (perhaps mistakenly) that it's not the spirit of this forum to leave threads with erroneous conclusions.

But, well, this isn't the first time (and I suspect it won't be the last) that I've been severely criticized for something that seems perfectly normal to me.

2. I'm surprised that you'd misinterpret this so,

I'm sorry, but I can't see exactly what I misinterpreted.

 

[Bandersnatch]

I'm sorry, but I can't see exactly what I misinterpreted.

Other than mentioning you in passing, I addressed the person I quoted.
There's no need to get all up in arms over my remark. Your clarifications are all kosher. I'm merely bemused by the why of anyone wanting to respond to people who have long left the building.

As an aside, a 'X' dominated universe, afaik, may refer to a universe with that X being merely larger than any other density, by also a universe where any density other than the X is negligible. In the latter case, a dark energy dominated universe would be equivalent to (or asymptotically approaching) a de Sitter one.

 

[Jaime Rudas]

Other than mentioning you in passing, I addressed the person I quoted.
There's no need to get all up in arms over my remark. Your clarifications are all kosher.

Sorry, but in your post #7, it's not at all clear that in point 1 you're referring to one person and in point 2 to another.

I'm merely bemused by the why of anyone wanting to respond to people who have long left the building.

In post #4 (which revives the thread), I'm responding to @Orodruin, who, as far as I know, hasn't left "the building".

As an aside, a 'X' dominated universe, afaik, may refer to a universe with that X being merely larger than any other density, by also a universe where any density other than the X is negligible.

I disagree. The current standard cosmological model is considered a dark energy dominated universe, and its dark matter content is far from negligible.

 

[PeterDonis]

Sorry, but in your post #7, it's not at all clear that in point 1 you're referring to one person and in point 2 to another.

He wasn't. All of his response (except for mentioning you in passing, as he said) was to what he quoted from another user, not you.

I disagree.

I don't think you do. I think you are just saying that our best current model of our actual universe is dark energy dominated in the first of the two senses that @Bandersnatch described. Since he did not claim that our actual universe was dark energy dominated in the second sense, nothing he said is inconsistent with what you said.

 

[PeterDonis]

1. this is an old thread - I'm not sure it's worth trying to engage with posts from close to two years back. Shame on Jamie for resurrecting the thread for no good reason.

This is not an appropriate comment. If you think an old thread should not have been restarted, please use the Report button to bring it to the attention of the moderators instead of making this kind of comment in the thread. (What's more, it's not very consistent for you to first say the thread shouldn't have been restarted, and then continue the restarted discussion.)

Having looked at the recent posts, I don't see any issue with this thread having been restarted. So it's fine to continue participating.

 

[Jaime Rudas]

I don't think you do. I think you are just saying that our best current model of our actual universe is dark energy dominated in the first of the two senses that @Bandersnatch described. Since he did not claim that our actual universe was dark energy dominated in the second sense, nothing he said is inconsistent with what you said.

Yes, you're right.

 

[Orodruin]

I disagree. The current standard cosmological model is considered a dark energy dominated universe, and its dark matter content is far from negligible.

This is a matter of nomenclature. When you refer to our universe as dark energy dominated, the meaning is exactly that dark energy is just the largest component. However, in general usage, it is typically also used to refer to a situation where other components are negligible. This is the kind of situation I was referring to in my post so I don’t really see that anything was added on top of that apart from perhaps clarification of meaning the latter case

 

[Hornbein]

I'm merely bemused by the why of anyone wanting to respond to people who have long left the building.

I always consider the Richard Nixonesque silent majority of readers to be my true audience.