Is the expansion accelerating or decelerating?

[Yashbhatt]

According to Hubble's Law, the farther a galaxy is, the farther it is moving away. But do we take into account the fact that we are actually looking in the past?

For example, there are two galaxies A and B at distance of 5 and 10 billion years respectively. Now, when we observe A we are looking at how it was moving 5 billion years ago. The same applies for B. So, now we conclude that 5 billion years ago space was expanding at a slower rate while it was expanding comparatively faster 10 billion years ago. What's wrong with this conclusion?

 

[Chronos]

That is why we observe. Our models are built on vetting observation v theory. Physicists generally concede that observation trumps theory.

 

[marcus]

According to Hubble's Law, the farther a galaxy is, the farther it is moving away. But do we take into account the fact that we are actually looking in the past?

For example, there are two galaxies A and B at distance of 5 and 10 billion years respectively. Now, when we observe A we are looking at how it was moving 5 billion years ago. The same applies for B. So, now we conclude that 5 billion years ago space was expanding at a slower rate while it was expanding comparatively faster 10 billion years ago. What's wrong with this conclusion?

The reasoning is logical but based on faulty assumptions about the definition of the terms in Hubble's law. v = H D
The law is stated in terms of present distance D you would measure if you could PAUSE EXPANSION long enough to measure by any conventional means, radar, a long tape, yardsticks. This is called the proper distance
The speed v is the speed NOW that the proper distance (i.e. the distance NOW) is growing.

So there is nothing about the past actually in the Hubble LAW. Of course in order to check the law and estimate the present value of H we have to have a model of how H(t) changes over time and we have to fit the model to data, which involves how things were in the past.

Taking account of the time-dependence, the Hubble law can be written v(t) = H(t) D(t)

At some time t, which could be a time in the past, the distance to the galaxy was D(t) and the Hubble rate was H(t) and the speed the distance D(t) was growing was v(t), which was equal to H(t)D(t)

That is what is fitted by a complicated process to the accumulated data.

But what I want to stress is that when we say that the distance to a galaxy is 5 billion light years or 5 Gly we do NOT mean that the light took 5 billion years to get here and that we are looking at the galaxy as it was 5 billion years ago. We mean that the distance you would measure to the galaxy NOW, if you could stop the expansion process to measure, would be 5 Gly.

That is the so-called proper distance and that is what the v = HD law is talking about.

 

[Yashbhatt]

I din't understand what you mentioned in the last paragraph. And is the Hubble constant "constant" over time?

 

[marcus]

... And is the Hubble constant "constant" over time?

No! It has changed enormously over time!

It's my bedtime so can't write more at present.

You could click on the "Lightcone" link in my signature at the end of this post and get an idea of how much H(t) has changed. the column labeled "R" essentially gives the RECIPROCAL of H, so when H was very big, in the past, R was very small. If you click on the link you will see how small.

Maybe someone who is awake will explain what some of the columns in the table mean

try hovering the cursor over some of the blue dots, they give some explanation

try increasing the number of steps, and recalculating, that way you get or more detail.

try clicking on column selection and definition, you get a menu with more explanations

Anyway I'm off to bed, Good Night :^)

 

[Yashbhatt]

The distance which is to be plugged in the equation v = Hd, is it the current distance to the galaxy or the distance to the galaxy when the light was emitted?

 

[Chalnoth]

The distance which is to be plugged in the equation v = Hd, is it the current distance to the galaxy or the distance to the galaxy when the light was emitted?

The time coordinate is the same on either side. If you plug in the distance when the light was emitted, and the expansion rate when the light was emitted, you'll get the recession velocity when the light was emitted. Same for if you use the parameters for the current time.

 

[marcus]

The distance which is to be plugged in the equation v = Hd, is it the current distance to the galaxy or the distance to the galaxy when the light was emitted?

If we are talking about the present-day value of the Hubble parameter (around 70 km/s per Mpc) then for sure the distance d to be plugged in is the distance TODAY :^D

and for the speed v, what you get is the speed at which that today distance is growing TODAY.

I'm reiterating what I tried to say earlier, and which Chally just now said again.

I'll bet you would enjoy some hands-on experience with the standard cosmic model, which is implemented in various online calculators, like Jorrie's Lightcone (link in my sig) or in Ned Wright's UCLA version (google "Wright cosmocalc" or something like that,maybe "wright calculator" would do). I happen to think Jorrie's is better but they are based on the same formulas and give essentially the same numbers. Jorrie's just makes tables of the universe history, so it gives you more.

 

[Yashbhatt]

So, what we do is measure a galaxy's distance to us. Suppose, we find that the galaxy is x billion years away So, we conclude that it's recession velocity at that time must be Hx. Then, we run the same equation forward in time and calculate it's present distance. Then, we again calculate it's recession velocity at current time based on Hubble's Law. Is that correct?

 

[Chalnoth]

So, what we do is measure a galaxy's distance to us. Suppose, we find that the galaxy is x billion years away So, we conclude that it's recession velocity at that time must be Hx. Then, we run the same equation forward in time and calculate it's present distance. Then, we again calculate it's recession velocity at current time based on Hubble's Law. Is that correct?

Well, we don't ever measure the proper distance itself. The proper distance is inferred from other measurements.

For example, if we know the true size of a far-away object, and we know how large it appears on the sky, then that gives us the angular diameter distance. The angular diameter distance is related to the current proper distance by a multiple of the scale factor.

One example here is SN1987A. Before the supernova, the star's violent behavior expelled a couple of rings of material. The supernova lit up those rings approximately one year after we saw the supernova, so we know that those rings were about a light year away from the star at the time they were illuminated. The Hubble telescope was able to view these rings in detail, allowing us to infer a distance of 168,000 light years for the supernova (note that in this case the amount of expansion over a period of 168,000 light years is small enough as to be irrelevant in the measurement: 0.001%).

Other measurements make use of the luminosity distance, which is a distance inferred from how bright an object appears compared to how much light it emitted at the source. This distance is a multiple of the scale factor squared different from the proper distance.

 

[Yashbhatt]

I think I messed up the time scale in the original post, right?