Why Does the Hubble Sphere Expand Despite the Changing Hubble Constant?

[gangula pranav]

why does the Hubble sphere increase amd why is the Hubble constant called a constant if the value keeps changing.

 

[marcus]

why does the Hubble sphere increase amd why is the Hubble constant called a constant if the value keeps changing.

In the standard cosmic model, the Hubble expansion rate is constant over all space at any particular moment of universe time. So you could call it "constant" (and people do) even though that
is a bit misleading. It does change gradually over time.

The standard model (called LCDM "lambda cold dark matter) involves simplification (it assumes a uniform distribution of matter and a simplified geometry) but it gives a remarkably good fit to the observational data. It is based on a simple differential equation (called Friedmann equation) that governs the expansion rate H(t) and determines how it changes over time.

The standard Friedmann model has a universal time parameter, which is a simplification. The general theory, as you probably know, has no preferred clock, no standard time, no preferred frame. So one wouldn't be able to talk about the universe at some given moment. But in LCDM, the standard model that cosmologists actually use, there is a preferred cosmic time parameter and one can talk about the universe at some given time t. And the Hubble growth rate H(t) is constant over all space.

Why does the Hubble sphere increase? Well the Hubble radius R(t) is essentially the RECIPROCAL of the Hubble expansion rate H(t). Actually 1/H is a TIME (so-called Hubble time) and multiplying it by c gives a distance, the Hubble radius.
R(t) = c/H(t)

So if the growth rate H(t) decreases, the Hubble radius naturally has to increase.

Notice that the Hubble growth rate H(t) is a fractional distance growth rate. IT SAYS BY WHAT FRACTION OF ITSELF A DISTANCE WILL GROW PER UNIT TIME. So it is always a number per unit time. Like "0.01 per million years" or one can express that as a percentage growth rate as in "1% per million years". That was the size of the growth rate when the universe was only a few tens of millions years old. More exactly, about the year 65 million.

And then later it was 0.005 per million years (I.E. 1/2 % per million years)
and then later 1/100 of a percent per million years, and so on.
It continues to decline. It must decline according to the Friedman equation and this checks out with OBSERVATION very nicely. We see that it has because the model gives a good fit.
Also it is forced by General Relativity, because the Friedmann is just a simplified version of the GR equation. It is derived from GR.
The gravity of the matter in the universe gradually reduces the percentage growth rate.
That is the key to what you asked. Since the percentage growth rate is decreasing (it is now about 1/144% per million years, and its reciprocal is 14.4 billion years) its reciprocal must be increasing!

However the decline in percentage growth rate is has slowed down over time, so true decline is now very very slow and it is tending to level out at some longterm rate (estimated at 1/173% per million years).

So for practical purposes the growth rate is ALMOST constant, and therefore distance growth is ALMOST exponential. Therefore if you could choose some given distance and watch it grow in size it would grow by increasing amounts proportional to its size, as it got larger. So its growth SPEED would increase, as it got larger. Even though its percentage growth RATE was gradually declining.

 

[ganguly pranav]

sorry for changing name and account (lost my password),anyway it is said that the expansion rate is increasing which obviously means that the Hubble constant is increasing but you said that the distance growth rate is reducing

 

[marcus]

... it is said that the expansion rate is increasing which obviously means that the Hubble constant is increasing...

It is not said that the expansion rate is increasing, if "rate" means the Hubble rate. When they say "expansion is accelerating" they mean if you watch a given distance grow in size, over time, its SPEED of expansion is increasing.

This type of acceleration can be happening to the expansion speed of a typical distance even though the percentage growth rate is declining, as it in fact is.

If you think people are telling you that the Hubble constant is increasing, then two things: either (1) you are confused and not listening carefully, or (2) popularizers should use different words, use more clear language, so they wouldn't give the public the wrong impression.

Take another look at what I wrote here, in post #2, and see if you find it understandable:
==quote post #2==
The gravity of the matter in the universe gradually reduces the percentage growth rate.
That is the key to what you asked. Since the percentage growth rate is decreasing (it is now about 1/144% per million years, and its reciprocal is 14.4 billion years) its reciprocal must be increasing!
However the decline in percentage growth rate is has slowed down over time, so true decline is now very very slow and it is tending to level out at some longterm rate (estimated at 1/173% per million years).

So for practical purposes the growth rate [although declining] is ALMOST constant, and therefore distance growth is ALMOST exponential. Therefore if you could choose some given distance and watch it grow in size it would grow by increasing amounts proportional to its size, as it got larger. So its growth SPEED would increase, as it got larger. Even though its percentage growth RATE was gradually declining.
==endquote==

 

[ganguly pranav]

thank you very much

 

[CygnusX-1]

why is the Hubble constant called a constant if the value keeps changing.

No astronomical constant is constant for all time. For example, the solar constant will be much greater in the far future, as the Sun becomes brighter. And a solar mass will be a lot less when the red giant Sun begins losing mass.

Since the Hubble constant is an astronomical constant, one shouldn't expect it to be constant for all time.

In contrast, physical constants--such as the speed of light, the charge on an electron, or Planck's constant--are indeed constant, as far as we can tell.

 

[ganguly pranav]

if the speed of the expansion is decreasing then it would mean that the radius of the Hubble sphere is increasing because it would require more space to expand faster than the speed of light .but as you said if the speed of expansion is increasing then why is the Hubble sphere increasing and
why is the radius of the Hubble sphere derived multiplying the speed of light with the Hubble constant where, the the Hubble constant is just the percentage of which the space is increasing while all we need to calculate the radius is the speed of expansion and not the percentage .


if gravity was the answer to my previous questions then does it mean that gravity will eventualy win over and stop the expansion and start bringing things together(leading to the big crush).If so then why is that the universe is expected to turn into a cold dark and empty place?would there be a big crush or the expansion just win over and turn the universe into a vast ,cold,dark,and empty place?