# On the 'constantness' of Hubble's Constant

I was reading Ned Wright's cosmology tutorial ( http://www.astro.ucla.edu/~wright/cosmo_02.htm ), and I'm a bit confused on how to interpret the diagrams featured on that page with respect to Hubble's constant.

As I understand, Hubble's constant basically expresses the (pretty much linear) momentary relationship between distance and recessional velocity of far-away objects, such as other superclusters.

Judging from the figures on Ned's site (scroll down a bit in that link: they show the expansion of space schematically in space-time diagrams, with our past light cone indicated by red lines), I'd say that Hubble's constant used to be larger in the past. After all, looking at the recessional velocity of objects at a certain fixed distance from 'our' position, this recessional velocity seems to get smaller over the course of time as the universe expands.

It could, of course, very well be the case that I'm making some wrong assumptions about those diagrams, but it seems logical to me that linear expansion of space (linear both in space and time) automatically means that Hubble's constant should decrease over time. If it stays constant, we'd be in an exponentially expanding universe, not a linear one. A decrease of Hubble's constant over time would even be compatible with an accelerating expansion (as we are apparently observing to be the case with our universe), that acceleration being within certain limits.

Of course we don't have direct observational data on the evolution of Hubble's constant with time (or do we?), but is it generally thought to be decreasing over time? Funny it should be called a 'constant', in that case: constant over space, rather than over time.

marcus
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... I'd say that Hubble's constant used to be larger in the past. ...
... is it generally thought to be decreasing over time? Funny it should be called a 'constant', in that case: constant over space, rather than over time.

that's right, very MUCH larger in the past

Yes, it is generally thought to be decreasing over time.
Yes it is funny to call it constant. I try to always call it the Hubble parameter to remind myself that it is not constant over time. I notice other people calling it that sometimes as well, maybe it's a trend.

Brinx, to get a hands-on feel of how it has changed over time try this cosmology calculator
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

Morgan does not put in the default parameters for you, so you have to type in (0.27, 0.73, 71) for (matter, lambda, hubble).

Then you can type in any redshift z, and it will tell you what the hubble parameter was at the moment a galaxy emitted some light which we are now receiving with redshift z.

Redshift z is a handy index both of distance and of how far back in the past. So if you type in the consensus best-fit parameters and then say
z=6, you should get

that the galaxy or quasar which we are now seeing with redshift 6
WAS 3.9 billion lightyears away from us when it emitted the light
and it WAS receding from us at 2.75c when it emitted the light
and the hubble parameter at that moment was about 686 km/sec per Megaparsec

the rapid decline of the hubble in earlier times is exactly the reason why light emitted from
objects that were receding FTL at that time has nevertheless been able to reach us
so the decline of the hubble has a dramatic practical consequence

To make a simple story (not to take the Little Engine that Could storybook image too seriously) the light emitted would have initially been swept back, but it hung in there and eventually the expansion
slowed enough for it to at least not be swept back, and then after stubbornly persisting some more, it even
began to make progress and get closer to us, and today it finally arrived.
the decline of the hubble parameter from around 700 then to around 70 now is what allows this to happen
it is a commonly recognized thing but still kind of curious

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As so often though, this leads me to wonder about another, related matter. As follows from the cosmology calculator, and from the explanation you provided, light emitted from objects which had recession speeds greater than 'c' at the time of emission can still reach us in certain cases, due to the gradual lowering of the Hubble parameter (I'll adopt the term too, I suppose!) over time. My new question is whether there are (hypothetical, because they may never be observable) areas of the universe of which the light emitted at any point in time will never be able to reach us? I suppose this depends on the projected future evolution of the Hubble parameter. Although it is getting smaller (at an ever slower rate, as I understand), this doesn't directly mean that all areas of the universe will be in view of eachother at any future point in time, as a decreasing Hubble parameter can exist within an ever more rapidly expanding universe...

marcus
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...whether there are (hypothetical, because they may never be observable) areas of the universe of which the light emitted at any point in time will never be able to reach us? ...

yes, according to the prevailing LCDM cosmology model (Lambda cold dark matter)

there is an article by C. Lineweaver around 2004 called "Inflation and the CMB" which has a clear explanation of this

it is called the "cosmological event horizon"

I have to go, maybe you can find the article by lineweaver on
http://arxiv.org/search

or someone else can provide a source

wikipedia might work too

marcus
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yes, thankyou Chronos.

there is a figure that shows diagramatically how the past lightcone, the hubble radius, and the "cosmological event horizon" are shaped in time, in particular shows that the lightcone is teardrop shape.

it is one of the earlier figures in the paper, I forget if it is Figure 1 or some other.

It also shows how the "particle horizon" expands with time. this is the farthest distance away that some crud could be, at present, if we could in principle be receiving light from it today (but in practice the early universe is opaque so we cannot get light from it)

another way to think of the "particle horizon" is to imagine that at the very beginning of expansion (the big bounce, in quantum cosmology terms) the crud that would later become Milkyway and us earth creatures sent out a flash of light or some other signal traveling at that speed----then the particle horizon is HOW FAR THAT WOULD HAVE GOTTEN measured in todays distance.

so there are all these distances to know about

particle horizon: todays distance of farthest crud we could now in principle be seeing light from

event horizon: todays distance of farthest events we will EVER witness no matter how long we wait---i.e. till infinity.

hubble radius: todays distance of crud that is receding at speed c.

Chronos
Gold Member
An interesting articulation marcus. The teardrop shape suggests our observable universe may be a pinched off bubble of a 'larger' universe [multiverse]. Most cosmologists concede this point to avoid dealing with 'initial conditions' problems - realizing they are merely pushing it outside the observable universe, not solving it. I don't object to that proposition. A universe much 'larger' than our observable universe is certainly possible, and probable from a quantum perspective. While the surface of last scattering is an indisputable limit on our observable universe, there is no evidence we can [or will ever be able to] observe it in it's entirety.

marcus
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An interesting articulation marcus. The teardrop shape suggests our observable universe may be a pinched off bubble of a 'larger' universe [multiverse].
to reply to your post Chronos. The teardrop shape does not suggest that to me.
My view would be that our entire universe MAY be a pinched off region (as in Sean Carroll's notes to his recent talk) but that would be for other reasons. The lightcone is not a picture of the universe, it is just the lightcone. It has teardrop shape simply because the universe has a history of expansion.

Most cosmologists concede this point to avoid dealing
I am not aware of "most cosmologists" conceding that point. Havent heard a lot of them "conceding" it. Would not be able to guess what their motivation would be, so can't judge whether your looking into their minds for the motivation is correct..
A universe much 'larger' than our observable universe is certainly possible, and probable from a quantum perspective.
I am glad you think so.

While the surface of last scattering is an indisputable limit on our observable universe,...
that is not true, if you mean what is technically possible to observe.
In cosmology writings the surface of last scattering always refers to the surface of last scattering of CMB light.
It is not the limit of what is technically possible to observe.
One can get other (non-light) signals from beyond where the CMB originated.

Such differences aside. I expect we agree on the elementary proposition that a satisfactory cosmology model must cover substantial regions that we cannot directly observe.
If the model were arbitrarily cut off at the limits of observation it would probably work very poorly. And indeed the usual mainstream LCDM model goes way far out beyond the range of observation---it models an organic whole. We can only verify it by comparing prediction to data in the sector we can observe.

===============

Neutrinos, of course.
Right!

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Chronos