Redshift: Is the Universe Slowing or Accelerating?

[PZIG98]

Just a physics buff so bear with me, this has been bothering but I am sure there is a simple answer.

I watch a lot of physics and science programs on TV. When discussing red shift the explanation is that the light from objects that a further away is more red-shifted than light from closer objects.

The conclusion is that the Universe is accelerating…

But, my question is, isn’t this telling us that older light is more red shifted than younger? And that the Universe is slowing down..?

Or is it that over time the amount of red shift increases? I.e. light from a particular star is more red-shifted today than it was 20 years ago?

 

[mgb_phys]

I watch a lot of physics and science programs on TV. When discussing red shift the explanation is that the light from objects that a further away is more red-shifted than light from closer objects.

Correct and that's fairly easy to show. Very distant objects have spectral lines that are shifted so far that we only see very distant galaxies in the infrared.

The conclusion is that the Universe is accelerating…

Not quite - the relationship just shows that the universe is expanding. More distant objects have larger redshifts and so are moving faster. Speed is proportional to distance = Hubble's law

But, my question is, isn’t this telling us that older light is more red shifted than younger? And that the Universe is slowing down..?

There are a few theories suggesting other non-cosmological sources for redshift. Most are based around the physical properties of atoms being different in the early universe - none of them have any scientific evidence.

Or is it that over time the amount of red shift increases? I.e. light from a particular star is more red-shifted today than it was 20 years ago?

The amount the star moves due to the expansion of the universe over a short time is much less than it's random motion due to the motion of other stars around it.

 

[PZIG98]

I think I am still missing something here...

Hubble's law, In laymen terms, says that the more distant an object the more red shift correct?

My confusion is, when light from more distant stars is observed we are looking at older light. So my thinking is that the "shift" occurred longer ago than the light observed form a closer object...

Makes me think that, longer ago, obects were moving away faster...

I know I am wrong but I don't know why...

Is red shift not a measure of velocity at the moment the light left the object?

If a star 1 million light years away suddely stopped moving away from us, we wouldn't see a change in the red shift for 1 million years...

 

[mgb_phys]

Sorry I thought you were implying that the redshift was a function of time - in that 'ancient' light was different to modern light.

Yes - Hubble's law says that distance is proportional to speed is proportional to redshift.
It's not that objects were moving away faster long ago it's that the universe has increased in size and so the light is 'stretched out' more. Older objects are at a larger distance = light more stretched out = faster speed relative to us.

 

[PZIG98]

So you are saying that the "Fabric" of space is what causes the shift and not the velocity of the object from which the light originated?

 

[mgb_phys]

It's the relative velocity between the object and observer - so you do get a redshift even from radio signals from a satelite - but in the case of distant objects, yes it's the expansion of the universe that gives them a recession velocity.

 

[PZIG98]

So then, If the Universe suddenly stopped expanding. How long would it take for us to see this via observations from my hypothetical star 1000 light years away?

 

[Chalnoth]

So then, If the Universe suddenly stopped expanding. How long would it take for us to see this via observations from my hypothetical star 1000 light years away?

Stars a thousand light years away aren't expanding away from us: they're within our own galaxy. You have to go to galaxies far away, many millions of light years out, to see the expansion at all. So in this impossible thought experiment, it would take many millions of years to see any stop.

 

[PZIG98]

Ok then, so 100 billion light years away...

The gist of the question is, would the delay be equal to the distance in light years?

 

[sylas]

Ok then, so 100 billion light years away...

The gist of the question is, would the delay be equal to the distance in light years?

Your question previously included the rider "if the universe stopped expanding". That's a rather incredible assumption... the forces required to stop a whole universe in its tracks are ... uh ... big. But hey.

If the universe was not expanding (as Einstein originally proposed with his cosmological constant) then yes, the delay would be the distance in light years. But there's another problem with this hypothetical "no expansion or contraction" state... it is unstable, like a pencil balanced on a point.

It would probably be useful for you to look at an introduction to cosmology. I personally like Ned Wright's Cosmology Tutorial.

Many of your questions here deal with things that are a consequence of expansion in general, and have nothing to do with whether this expansion is accelerating or not. For example, you say that "long ago, objects were moving faster".

But that's not the reason for the redshift distance relation. It is rather that the nature of expansion means that things further away from us are receding faster. The "oldest" light is from the most distant objects, and they have the greatest recession velocities. That's true, whether expansion is accelerating or decelerating. You need to work a bit more on what expansion means before the accelerating or deceleration of expansion will make much sense.

Cheers -- sylas

 

[PZIG98]

Thanks for the link.

Unfortunatley, My understanding, or lack there of, expansion comes not from classrooms and lectures but watching too much science channel...

So, my concept of expansion is dots drawn on a baloon... But even with that it is not too difficult to grasp more separated objects growing apart faster than less separated objects...

Knowing that, then more distant objects would have more red shift that those that are less distant regardless of exceleration? So, This difference in red shift is greater than expansion can account for? Therfore, Exceleration?

 

[sylas]

Thanks for the link.

Unfortunatley, My understanding, or lack there of, expansion comes not from classrooms and lectures but watching too much science channel...

So, my concept of expansion is dots drawn on a baloon... But even with that it is not too difficult to grasp more separated objects growing apart faster than less separated objects...

Knowing that, then more distant objects would have more red shift that those that are less distant regardless of exceleration? So, This difference in red shift is greater than expansion can account for? Therfore, Exceleration?

I'm not sure I can really follow this. Expansion is not something different from accelerating expansion, so the difference in red shift between distant galaxies and very distant galaxies is always explained with expansion. Acceleration (a change in the rate of expansion) is detected by some rather subtle consequences for the relation between redshift, luminosity and angular size in distant galaxies, and that's tough to explain quickly.

There are different analogies that people use to try and explain expansion. One of them is the loaf of rising bread. Raisins in the bread are moving apart from each other in the same way that galaxies are moving apart from each other. It is a feature of rising bread that the rate at which any two raisins are separating from each other is proportional to the distance between the raisins. Same with galaxies... the most distant galaxies are the ones moving away the fastest.

Every analogy has problems. In this case, the analogy omits the fact that galaxies are also moving locally with random motions.

What acceleration or deceleration means is that the rate at which expansion occurs is changing. With galaxies, when you look at very distant galaxies you are also looking back in time, to when everything was closer together. The relationship between the recession velocity and the density will tell you how the rate of expansion is changing with time. That's not quite how it is done by astronomers, but it's part of it.

Generally speaking, we would expect the gravitational attraction of objects in the universe to pull everything back together and slow the rate at which they are expanding apart. Surprisingly, the opposite seems to be occurring, as if there is a "dark energy" that gives things an extra kick to keep moving apart a bit faster as time goes by. But long before the observations that suggested this dark energy, back about twenty years ago when it was conventionally expected that expansion was slowing, we STILL had the case that the most distant galaxies had the greatest recession velocities.

Cheers -- sylas

 

[PZIG98]

Thanks Syals, I get what you are saying...

I think what crosses my eyes is that we are infering through measurements of acient light what is happening at the outer edges of the observable Universe today.

I also understand that I don't know enough about it to argue one way or the other. But I do appreciate you all taking the time help clear or perhaps further muddy the waters...

 

[sylas]

Thanks Syals, I get what you are saying...

I think what crosses my eyes is that we are infering through measurements of acient light what is happening at the outer edges of the observable Universe today.

I also understand that I don't know enough about it to argue one way or the other. But I do appreciate you all taking the time help clear or perhaps further muddy the waters...

Heh. With that encouragement, I'll try to muddy or clear the waters some more!

The oldest light of all is the "cosmic background radiation". The photons were emitted back when the universe was a bit less than 400,000 years old, and about 1100 times more compressed than it is at present. At that point, there were no galaxies or stars; the whole universe was a seething mass of hot ionized gas -- mostly hydrogen. Ionized hydrogen is opaque. But as the universe expands and cools, the gas was able to hold on to electrons, and became neutral hydrogen gas... which is transparent. The light emitted from that time has been traveling ever since, and now fills the universe with a background of microwave radiation. The redshift involved with these photons is enormous.

We presume, reasonably enough, that the gas we "see" though this radiation is the same kind of gas that condensed and formed our own local region of space, and so it is a picture of what things were like in our own past. But if that gas condensed into galaxies in the same way, those galaxies will be much much further away than any galaxies we can see at present.

If you tune an old TV to the static between channels, about 1% of the "snow" you see on the screen is microwave radiation from the very early universe. This marks the edge of the observable universe (as far as light is concerned); though there are other prospects than light for "looking" even further back in time... if and when we are able to detect and measure gravitational radiation.

I find that awe inspiring.

Cheers -- sylas

 

[PZIG98]

As do I and suppose that is why I watch too much Science Channel, Discovery etc...

I never got a good grasp of algebra in High School and often wish to try again so that I might better be able to read the equations that discussions like this inevatably lead to.

While we talk about the edge of the observable Universe I find it equaly awe inspiring to think about the smallest of small and what exactly the fabric of space and time really is and if what we call matter is simply that space and time behaving differently...

 

[keepitmoving]

i`m just an amateur here but as i understand it, the far away (high redshift) galaxies were accelerating less at the time the light left than the nearby galaxies are accelerating now. The faraway galaxies maybe were moving faster , but they aren`t accelerating faster, matter of fact, their acceleration was negative in the past but that doesn`t mean that a given object didn`t move away faster in succeeding million years periods. It did. I think it`s the second derivative that is what the acceleration is talking about.

 

[PZIG98]

I undertsand the opposite to be true.

The further away an object is from you the faster it is moving away from you, or you from it... (The raisin bread scenario above).

I'll probably get this wrong but, Think of two opposite sides of a balloon that is being filled at a steady rate. As the Balloon's volume expands, points on the two opposite sides grow further apart at an accelerated rate. That is for every equal period of time, the distance grows at an ever increasing increment...

Accelerated expansion means that the balloon's volume is also expanding at an ever increasing rate. Some extra(dark) energy is being added along with the air that is filling the balloon...

Anyway, that is my simple misunderstanding :)

 

[ideasrule]

I undertsand the opposite to be true.

The further away an object is from you the faster it is moving away from you, or you from it... (The raisin bread scenario above).

I'll probably get this wrong but, Think of two opposite sides of a balloon that is being filled at a steady rate. As the Balloon's volume expands, points on the two opposite sides grow further apart at an accelerated rate. That is for every equal period of time, the distance grows at an ever increasing increment...

Accelerated expansion means that the balloon's volume is also expanding at an ever increasing rate. Some extra(dark) energy is being added along with the air that is filling the balloon...

Anyway, that is my simple misunderstanding :)

If a balloon's volume increases at a constant rate, its radius actually increases at a decreasing rate. When cosmologists say the universe is expanding, they mean that any two (distant) points in the universe are moving apart, not that the universe's volume is increasing. The universe might have infinite volume, for all we know.

Acceleration of expansion means the rate at which two points in the universe move apart is increasing with time. In other words, instead of increasing by 1% every x million years, it may now increase by 1% every x-1 million years.

 

[sylas]

If a balloon's volume increases at a constant rate, its radius actually increases at a decreasing rate. When cosmologists say the universe is expanding, they mean that any two (distant) points in the universe are moving apart, not that the universe's volume is increasing. The universe might have infinite volume, for all we know.

Acceleration of expansion means the rate at which two points in the universe move apart is increasing with time. In other words, instead of increasing by 1% every x million years, it may now increase by 1% every x-1 million years.

Um... don't use a "percent". Increasing by a fixed percentage per unit time is pure inflationary expansion, which corresponds to accelerating exponentially.

To understand acceleration, think in terms of the scale factor. The scale factor is a dimensionless value, giving the ratio by of linear distances between co-moving points with respect to some reference. By convention, the scale factor is often take as 1 in the present.

Hence the scale factor in the past was 0.5 when (on large scales) things are twice as close together as at present. It will be 2 in the future when (on large scales) everything is about twice as far for everything else at at present.

The "velocity" of expansion (which is not a velocity, the units are inverse time) is the rate of change of scale factor. There's no acceleration when everything just keeps moving apart with the same motion.

The acceleration is the next derivative.

Matter and gravity will tend to slow the expansion down, as it pulls everything back together. Dark energy is a kind of pressure that gives an extra boost to things so that they tend to move apart more rapidly.

Cheers -- sylas

 

[ideasrule]

Um... don't use a "percent". Increasing by a fixed percentage per unit time is pure inflationary expansion, which corresponds to accelerating exponentially.

To understand acceleration, think in terms of the scale factor. The scale factor is a dimensionless value, giving the ratio by of linear distances between co-moving points with respect to some reference. By convention, the scale factor is often take as 1 in the present.

Hence the scale factor in the past was 0.5 when (on large scales) things are twice as close together as at present. It will be 2 in the future when (on large scales) everything is about twice as far for everything else at at present.

The "velocity" of expansion (which is not a velocity, the units are inverse time) is the rate of change of scale factor. There's no acceleration when everything just keeps moving apart with the same motion.

The acceleration is the next derivative.

Matter and gravity will tend to slow the expansion down, as it pulls everything back together. Dark energy is a kind of pressure that gives an extra boost to things so that they tend to move apart more rapidly.

Cheers -- sylas

The rate of increase in scale factor is the rate of percentage change. If the scale factor increases at 0.01/million years, that means the distance between 2 objects increases 1% per million years. I don't see how this leads to inflationary expansion, in which the time derivative of the scale factor, and the 2rd time derivative, and the third, and so on all increase exponentially with time.

 

[Chalnoth]

Knowing that, then more distant objects would have more red shift that those that are less distant regardless of exceleration? So, This difference in red shift is greater than expansion can account for? Therfore, Exceleration?

No. The expansion is there regardless. The acceleration is talking about the rate of expansion. That is, though our universe has been expanding for some 13.7 billion years or so, the rate at which it has been expanding has changed with time. At early times, shortly after the end of inflation, the expansion was decelerating rapidly: it was expanding, but the expansion was getting slower and slower. More recently, it has started to expand more and more rapidly.

This is demonstrated by looking at a variety of different measures of the rate of expansion as a function of time.

 

[sylas]

The rate of increase in scale factor is the rate of percentage change. If the scale factor increases at 0.01/million years, that means the distance between 2 objects increases 1% per million years. I don't see how this leads to inflationary expansion, in which the time derivative of the scale factor, and the 2rd time derivative, and the third, and so on all increase exponentially with time.

No, it isn't. Really.

If you have a function that increases by a fixed percentage, or factor, per unit time, then you have an exponential function. Think about compound interest.

Here are more technical details specifically on cosmology. The co-moving distance co-ordinate is unaltered by expansion. The scale factor is the ratio between proper distance and co-moving distance.

The scale factor is often written as "a", and it is a function of proper time. When you have constant expansion, with no acceleration or deceleration, the scale factor is a linear function of time. In this case, if you pick any two co-moving galaxies, they continue to separate at a constant velocity.

If you have the scale factor increasing by a fixed factor, or percentage, per unit time, then you have an exponential relation, corresponding to inflation.

Another well known simple model is the matter-critical flat model, with no dark energy. In this case the expansion is slowed by the effects of gravity, but not quite enough to stop expansion continuing to indefinitely.

The three solutions can be given as follows:

$$\begin{align*} a &= H_0 t & \mbox{Linear expansion; empty universe} \\ a &= e^{H_0 t} & \mbox{Exponential expansion; inflation} \\ a &= \left(1.5 H_0 t \right) ^\frac{2}{3} & \mbox{Matter critical expansion} \end{align*}$$​

The first case has no acceleration, and the scale factor increases by a fixed amount per unit time. The second case is accelerating, and the scale factor increases by a fixed percentage per unit time. The third case is decelerating.

The constant H₀ has units of inverse time, and it is actually the Hubble constant in more sensible units. It is equal to the first derivative of a at the time when a itself is equal to 1, typically chosen as the present.

The above should serve to address the matter of what acceleration means... here is a bit more technical stuff closer to what our universe is doing. Our own universe, as far as we can tell, behaves on large scales pretty much as given by the following differential equation:

$$\begin{align*} \frac{da}{dt} & = a H_0 \sqrt{ \Omega_M a^{-3} + \Omega_V } \end{align*}$$​

This is the FRW solution for a flat universe, with matter as a fraction Ω_M of critical and dark energy as a faction Ω_V of critical. There's a bit of work nailing down those parameters, but they seem to be about 0.27 and 0.73 respectively. You'll often see these numbers used in recent descriptions of modern cosmology; they are based on the WMAP experiment; and there may be slightly updated estimates used with recent more accurate work nailing down the Hubble "constant".

The Ω_V drives acceleration, and the Ω_M factor retards it. If you solve for the next derivative you get

$$\frac{d^2a}{dt^2} = H_0^2 a (\Omega_V - 0.5 \Omega_M a^{-3})$$​

In this model, the acceleration took over from deceleration when the scale factor was

$$a = \left(\frac{\Omega_M}{2 \Omega_V} \right)^\frac{1}{3} \approx 0.57$$​

 

[marcus]

...If you have a function that increases by a fixed percentage, or factor, per unit time, then you have an exponential function. Think about compound interest.

Here's an issue concerning explanatory language. I agree that unless one is careful to make clear that one is not talking about exponential growth it could be confusing to use a (non-fixed) percent to describe the current rate of expansion.

However (for better or for worse) over the past couple of years I have found it helpful to use a (current) percent rate as an alternative to quoting the current value of H in terms of km/s per Megaparsec.

If in conventional units you say that the current (and declining) value of H is 71 km/s per Mpc, then that translates by simple arithmetic into the statement that distances are currently increasing by about 1/140 of a percent every million years.

Using a percentage like that gets across to newcomers to the board the important idea that larger distances increase more. It's easy to visualize, and it also conveys the subliminal message that we are not necessarily talking about velocities, of galaxies going somewhere, but rather we are talking about uniform increase of distances.

This way of describing the current rate of increase of distance, as a declining percentage rate, currently 1/140 percent every million years, seems to me to have worked fairly well. On the other hand I would like to align my way of explaining with yours to some extent, and avoid dissonance. (We don't disagree on any technical or factual point as far as I can see, but do on a point of pedagogical language.)

So my question is, can I continue to describe the current Hubble rate this way, if I make clear that the percentage is slowly declining (we are not talking about straight exponential growth)?

 

[sylas]

This way of describing the current rate of increase of distance, as a declining percentage rate, currently 1/140 percent every million years, seems to me to have worked fairly well. On the other hand I would like to align my way of explaining with yours to some extent, and avoid dissonance. (We don't disagree on any technical or factual point as far as I can see, but do on a point of pedagogical language.)

So my question is, can I continue to describe the current Hubble rate this way, if I make clear that the percentage is slowly declining (we are not talking about straight exponential growth)?

I wouldn't presume to advise on that! Every situation is different, and the percentage rate of change is a good way to indicate that the rate of expansion is pretty slow. Good pedagogy adapts to the circumstances, in my opinion; and your reasoning makes sense.

Another way to show how slow expansion is might be to use different units. The expansion rate was recently estimated at 74 km/sec/MParsec.

A MegaParsec is an unfamiliar unit to lots of people... if you made it kilometers as well, the expansion rate would be 2.4*10^-18 km/sec/km.

But the percentage thing seems okay. After all, there's another little problem in explaining this measurement. The Hubble "constant" actually reduces with time when you have a fixed rate of expansion of scale factor. Over time, the Hubble "constant" in the units I have given here is equal to da/dt divided by a... and so the Hubble "constant" isn't constant at all... except in the special case of pure exponential expansion. So now we confuse people because with the current model of accelerating expansion, the Hubble constant is still reducing. Ah well. Any simple explanation has problems.

Cheers -- sylas

 

[marcus]

Thanks for the reassurance, Sylas! Tentatively I will continue talking about the Hubble rate that way especially with newcomers. I also put the question generally in a separate thread in case anybody else has opinion or advice.