# Hubble Parameter & acc. Universe

1. Jul 10, 2007

### sergei

Hubble "Parameter"& acc. Universe

I am a senior high student. And I am studying on SnIa.
I recently read that SOME(maybe most) theory said that hubble's constant is not a CONSTANT, it's changing by time.

But I wonder if there are something influent the data.
(like "slection effect" .etc)
==========================
But let's assume all the obs. data are fine and very precise.

We can simply conclude that Hubble's constant varies by time and the universeis accelerating
(In short,
H of cepheid=70, H of near Ia=50, H of far Ia=30)
So....
I have many question to ask.

0. The theory"hubble parameter is a value relate to time" is build on a "universe model" called (flat and ****...model), If anyone disagrees hubble parameter varies by time, does he either disagree this universe model?

1. If H really varies by time, can we ever measure the age of the universe by 1/h ?

2.If anyone disagrees that Hubble parameter varies by time, how does he describe the accelerating universe?(or he also disagree the accelerating universe)

3.And how do you explain this "calculated results"
(H of cepheid=70, H of near Ia=50, H of far Ia=30)

Despite the fact that what theory you support, it's welcome for you to give me ANY though of yours.

ps. I have asked a prof. that he said that there are still some people think hubble is a CONSTANT that never change, but they still can't "find" any powerful evidences or theories to prove their stance.

2. Jul 10, 2007

### cristo

Staff Emeritus
As you suggest, Hubble's parameter is a function of time. However, Hubble's constant, commonly denoted H0, is the value of Hubble's parameter at the present time. This is a constant, and it is the reciprocal of this that is the age of the universe.

Last edited: Jul 10, 2007
3. Jul 10, 2007

### sergei

I cant agree that the age is reciprocal of hubble constant(H0).
Eg. The constant of very-far(high Z) supernova Ia is about 30.
And those Supernovae is represented of many "thousand millions years' present"
But the reciprocal of 30 can refer the age of 320 hundred millions years old
As your thought, If I were at the time that the high Z is near my side. and the H I measured would be 30, then I refer from the reciprocal and say "The universe is 320000000 years old....."
Hope you know what I am talking about........

4. Jul 10, 2007

### sergei

If you were being in 60 hundred millions years ago, and measured the High-Z SnIa (as I mentioned above) And you would find that the H is 30 also.

(For the light need 60 hundred millions years to pass to present,2007; I will also measured the H of 30 by the High-Z)

NAMELY, Both our values of H are the same, And at your time(60 hundred millions years ago) your H is called H0 and mine is called H of 60 hundred millions years ago.

And at your time(60 hundred millions years ago),you would say the {reciprocal of H0} is denoted the time and you made a ridiculous conclusion, THE AGE OF THE UNIVERSE IS 300 hundred millions years old.

And at my time (present,2007) My Value of H0 is 76, and I concluded that the age is 120 hundred millions years old.

How about this explanation refer from your remark "" This is a constant, and it is the reciprocal of this that is the age of the universe.""？
I think it's totally wrong, as I have read there's a sentence says that "We can't simply refer the age of the universe by the reciprocal of H0"

5. Jul 10, 2007

### marcus

they happen to be very close, and I think one is a good rough estimate of the other---maybe in some simplified models they would be the same

but my cosmology teacher assured us that Hubble time and age are
actually not the same (it is more just coincidence that they are so close)

so I agree in this case with sergei
(although most times I agree with cristo who normally gives clear correct answers)

Last edited: Jul 10, 2007
6. Jul 10, 2007

### marcus

Sergei, the time evolution of H(t)
is governed by a famous equation called the Friedmann equation.

maybe you live in St Peterburg/Leningrad, the same city where Friedmann lived and many other famous mathematicians. Besides discovering the Friedmann equation he also won the high altitutude record for balloon flight.

Since you are studying these things and talking to professor about it, maybe you know this equation!

by definition H(t) = a'(t)/a(t)
and the left hand side of the Friedmann equation that I am talking about is the SQUARE of this quantity, (a'(t)/a(t) )^2

So already in 1923, Friedmann knew that the Hubble parameter changes and he knew HOW it changes, but unfortunately for him there was not yet any Hubble parameter because Edwin Hubble had not had the idea of it yet.

7. Jul 10, 2007

### sergei

Thanks a lot, marcus!!
I knew Friedmann equation, but it DOES relate to some model.
And I think when my physical skills and knowledge improve, I will try to know more about these theory and some models.

And I, wondering why IT IS DIFFICULT TO FIND MANY INFO ABOUT HUBBLE PARAMETER.(even in ENG,there is relatively much few data of "hubble parameter") (In my contury, there's almost none[very very very few] talking about hubble parameter)

I've seen this equ. But I cant figure out what the "a" should be.(parameter of universe expansion......)

But how he knew how the parameter changes? Do you mean that he conclude H to a equation like [H(t)= a'(t)/a(t)]?

I wonder if there are any theories AGAINST the accelerating Universe
(eg. FTL (Faster then light) theory...... haha)

8. Jul 10, 2007

### George Jones

Staff Emeritus
This is entirely correct. Call the present age of the universe t_0 and the present value of the Hubble constant H_0. Then, to a good approximation, t_0 = 1/H_0. This is just coincidental.

Notice that cristo does not say that the age of the universe at any given time t is the reciprocal of the of the value of Hubble constant at time t.

The Hubble constant is constant in space, not constant in time. At any instant in time, let L be the proper distance from us to any galaxy. Then, at any instant in time t, v/ L is constant for *all* galaxies, independent of their proper distance from us. At some other instant in time t', v/L is still constant, but is, in general, not equal to the constant at time t, i.e., the value of this (spatial) constant changes with time. This constant is the Hubble constant.

Also, the acceleration of the universe and rate of change of the Hubble constant are somewhat independent. For example, at the present time, the value of the Hubble constant is decreasing with respect to time, even though the expansion of the universe is accelerating with respect to time.

9. Jul 10, 2007

### marcus

Fair enough. what George says is right.

I was just joking when I said Friedmann found the Hubble parameter before Hubble did----but there is this term a'/a in the Friedmann equation and later this was the definition of the Hubble parameter, so it is "as if" he thought of it.

the basic thing you should learn about, if you don't know it already, is the FRW METRIC----the "Friedmann-Robertson-Walker metric"

the quantity a(t) is just a SCALE FACTOR in the FRW metric.

it is a spatial scale factor, so it governs how space expands---or more exactly how distances expand (since space is not a material it is confusing to say that space expands)

so as a(t) increases, all distances increase in proportion.
==============

the reason all definitions go back to the metric is that a solution to the basic einstein equation is a metric------the spacetime metric is just another name for the gravitational field, which must be a solution to the einstein eqn.

the FRW metric, which comes in various versions depending on a(t), is
just one particular solution to einst. eqn. It is one possible solution.
this is the solution that cosmologists typically consider. It simplifies their job. Then they only have to wonder what is a(t)
and that means they only have to study solutions of the Friedmann eqn. which is a very simple equation compared with the full Gen Rel.
-----------------

I am too lazy now to write down for you the FRW metric and the Friedmann equation. So you must find it by Google. Or else maybe someone here will be kind enough to write it using Latex.

I wrote Friedmann equation here, some time ago, in post #43