# Question about the Hubble Constant

• I
• Thecla
In summary, the Hubble constant, which represents the rate of expansion of the universe, decreases over time. This is due to the accelerating expansion of the universe, where the rate of change of the scale factor with respect to time is increasing. This means that far-away galaxies are moving away from each other at faster speeds. If humans existed 2.5 billion years ago with today's equipment, they would have measured a larger Hubble constant due to the universe being 20% younger and the expansion rate being larger in the past. However, it is predicted that the Hubble constant will eventually settle down to a constant value in the far future.
Thecla
TL;DR Summary
does the Hubble Constant change over time?
If there were humans on Earth 2.5 billion years ago (universe 20% younger) and they had today's equipment , would they measure the Hubble constant smaller, larger or the same?

Larger. It was always larger in the past, and will be always smaller towards the future.

Halc
It indeed will always be smaller in the future, but not arbitrarily smaller. It was arbitrarily higher in the past, especially in the first fraction of a second of the big bang.

I think I read that it is predicted to settle down to about 57 km/sec/mpc and go no lower. That's exponential expansion as opposed to the more linear expansion in the (fairly) recent past.
Of course if it continues to fall always, you end up with a big-rip finale.

Halc said:
Of course if it continues to fall always, you end up with a big-rip finale.
Big rip is when it starts growing without bound, surely.

Bandersnatch said:
Big rip is when it starts growing without bound, surely.
Duh, of course. Decreasing without bound happens with no expansion, such as the Milne solution.
Brain fart. Sorry.

Last edited:
jim mcnamara and Bandersnatch
Well, I might have clicked like too early ;)
You meant Milne solution? The one with no acceleration/deceleration (but with expansion)? The one where H decreases towards 0 (i.e. not without bound)?
Decreasing without bound leads to reversed expansion. I.e. contraction. A big crunch.

Thecla said:
Summary:: does the Hubble Constant change over time?

If there were humans on Earth 2.5 billion years ago (universe 20% younger) and they had today's equipment , would they measure the Hubble constant smaller, larger or the same?

To a good approximation, our universe presently is a (spatially) flat FLRW universe that consists of matter (##w=0##) and dark energy (##w=-1##). The scale factor for such a universe is
$$a\left(t\right) = A \sinh^{\frac{2}{3}} \left(Bt\right),$$
where ##A## and ##B## are constants. The Hubble parameter is
$$H = \frac{\frac{da}{dt}}{a}.$$
Can you use this to find and expression for the Hubble parameter? If not, I will (eventually) fill in the details

Halc said:
I think I read that it is predicted to settle down to about 57 km/sec/mpc and go no lower. That's exponential expansion
Yes.

Halc said:
as opposed to the more linear expansion in the (fairly) recent past.
The expansion was never linear. Before a few billion years ago, it was more or less parabolic (matter dominated, density near critical).

Halc said:
Of course if it continues to fall always, you end up with a big-rip finale.
No. If it continues to fall always, asymptoting towards zero, that would be a matter dominated universe with density less than or equal to critical and zero cosmological constant. That was the "best fit" model cosmologists were using until the late 1990s when the accelerating expansion was discovered.

If it continues to fall always and becomes negative, that would be a matter dominated universe with density greater than critical and zero cosmological constant--i.e., a closed universe that will recollapse to a "big crunch".

Halc said:
Decreasing without bound happens with no expansion, such as the Milner solution.
The Milne universe does have expansion; even though it is flat Minkowski spacetime in funny coordinates, the congruence of "comoving" observers in this universe has positive expansion. This universe is the limiting case of an "open" universe (density less than critical) when the density goes to zero.

PeterDonis said:
The Milne universe does have expansion; even though it is flat Minkowski spacetime in funny coordinates
Yes, but the expansion rate, expressed in km/sec/mpc, drops to arbitrarily low over time, even if never to zero. The Hubble constant is never a constant, at least not yet.

Halc said:
the expansion rate, expressed in km/sec/mpc, drops to arbitrarily low over time, even if never to zero.
Yes, that follows from the fact that this is a limiting case of an open universe.

I don't understand. If it were larger in the past, why do astronomers say that the expansion is accelerating. Shouldn't this mean the Hubble constant is increasing?

Thecla said:
If it were larger in the past, why do astronomers say that the expansion is accelerating. Shouldn't this mean the Hubble constant is increasing?
When astronomers talk about the expansion accelerating, they are talking about the rate of change of the scale factor with respect to time, i.e., ##\dot{a}##. "Accelerating" means ##\dot{a}## is increasing. But the Hubble constant is ##\dot{a} / a##, and that is decreasing. For the case that @George Jones gave the equation for in post #7, you should be able to calculate explicitly both of these quantities and confirm that what I have just said is true.

Thecla said:
Summary:: does the Hubble Constant change over time?

If there were humans on Earth 2.5 billion years ago (universe 20% younger) and they had today's equipment , would they measure the Hubble constant smaller, larger or the same?

Here is a H vs t plot:

Please see the thread, The Hubble constant − constant in what way?

PeterDonis said:
When astronomers talk about the expansion accelerating, they are talking about the rate of change of the scale factor with respect to time, i.e., ##\dot{a}##. "Accelerating" means ##\dot{a}## is increasing. But the Hubble constant is ##\dot{a} / a##, and that is decreasing. For the case that @George Jones gave the equation for in post #7, you should be able to calculate explicitly both of these quantities and confirm that what I have just said is true.
Another way to put this is the accelerated expansion means that far-away galaxies are moving away from one another at speeds that increase with time.

A constant expansion rate is one way to cause this to happen: constant rate means constant recession velocity over distance ratio. So increase the distance, increase the recession velocity.

As long as the rate of expansion (the Hubble parameter) is decreasing slowly enough, recession velocities will increase as things move away from one another. This is the case today. I'm the far future, if the dark energy behaves like a cosmological constant, the rate of expansion will become nearly constant.

Ibix
PeterDonis said:
When astronomers talk about the expansion accelerating, they are talking about the rate of change of the scale factor with respect to time, i.e., ##\dot{a}##. "Accelerating" means ##\dot{a}## is increasing. But the Hubble constant is ##\dot{a} / a##, and that is decreasing. For the case that @George Jones gave the equation for in post #7, you should be able to calculate explicitly both of these quantities and confirm that what I have just said is true.

Using Jorrie’s calculator, we can calculate a(t) and the Hubble parameter, H(t). The expansion rate can be calculated with the equation,

da/dt = a(t) H(t) (see Post #7)​

The results are plotted below:

The above figure suggests that, according to the ΛCDM model, the expansion of the universe is accelerating.

## 1. What is the Hubble Constant?

The Hubble Constant is a measure of the rate at which the universe is expanding. It is represented by the symbol H0 and is measured in units of kilometers per second per megaparsec.

## 2. How is the Hubble Constant determined?

The Hubble Constant is determined by measuring the distances to galaxies and their redshifts. The redshift is a measure of how much the light from a galaxy has been stretched due to the expansion of the universe. By combining these measurements, scientists can calculate the Hubble Constant.

## 3. Why is the Hubble Constant important?

The Hubble Constant is important because it helps us understand the age and size of the universe. It also provides evidence for the theory of the Big Bang and helps us better understand the evolution of the universe.

## 4. Has the value of the Hubble Constant changed over time?

Yes, the value of the Hubble Constant has changed over time as our technology and methods for measuring it have improved. In the 1920s, it was estimated to be around 500 km/s/Mpc, but now it is estimated to be around 70 km/s/Mpc.

## 5. What is the current accepted value for the Hubble Constant?

The current accepted value for the Hubble Constant is approximately 70 km/s/Mpc. However, there is still some debate and uncertainty surrounding its exact value, with some recent studies suggesting a slightly higher value of around 74 km/s/Mpc.

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