Help with when expansion acceleration began

[Rodney-Believes]

I read in Wikipedia that
"For supernovae at redshift less than around 0.1, or light travel time less than 10 percent of the age of the universe, this gives a nearly linear distance–redshift relation due to Hubble's law. At larger distances, since the expansion rate of the universe has changed over time, the distance-redshift relation deviates from linearity, and this deviation depends on how the expansion rate has changed over time."

If the expansion of space is stretching the light traveling through it (creating the red-shift), and acceleration began about 5 billion years ago, then why is the most recently emitted light "nearly linear distance-redshift relation"? It would seem that within expansion, which is red-shifting the light, acceleration began recently, then the newer light would red-shifted under an acceleration, so why is it more linear? The "older" light, which would have traversed the universe through both steady rate (or decelerating) and accelerating. It should be closer to linear depending on how very distant, how much more of the red-shift came from steady-rate vs accelerating.

In other words, if in observation the newer light is "nearly linear" and the older light is not, and it is the expansion that is shifting the frequency of the light, that would suggest to me that the universe was once accelerating but has become more steady rate in recent times. Can someone set me straight on this?

Thank you.

 

[Orodruin]

The redshift only depends on the relative scale factors at emission and observation. For any differentiable function, $f(t) \simeq f(t_0) + f'(t_0)(t-t_0) + \mathcal O(t-t_0)^2$, which means that the particular form of the function does not matter. For small times the main effect is going to be linear.

 

[Rodney-Believes]

Thank you for the help, but I don't yet understand.

If that is so, then the observation of linear by newer light is simply because of closeness, it's not really steady speed (linear), current acceleration is not big enough to show up at closer distances. So, still, how does this observation help us to know when the Universe began accelerating? If "for small times the main effect is going to be linear", then how can we compare it to longer travel times, where acceleration has time to show up, and use that to say "it started accelerating recently"? The statement is that it used to not be accelerating but started in the more recent age of expansion. Yet, the older light shows none linear recession?

 

[Orodruin]

You have to look at the entire history of redshift vs luminosity, not only on nearby objects. The history reveals the functional behaviour of the scale factor.

 

[Ibix]

For any smooth curve, you can fit a straight line over a range where the curve doesn't deviate too far. You get much simpler mathematics, and you just live with small errors since they're smaller than your measurement error and other uncertainties anyway.

Apparently for redshift data the range you can get away with pretending there's no acceleration given current measurement accuracy is 10% of the age of the universe. It isn't related to acceleration starting or stopping. It's related to the acceleration term having an unmeasurably small effect on light from nearby sources.

 

[Rodney-Believes]

I'm really sorry for pressing, but I want to understand.

From Wikipedia, "this deviation depends on how the expansion rate has changed over time." Whoever wrote this was offering this observation as how we know when acceleration started.

Ibix wrote, "It's related to the acceleration term having an unmeasurably small effect on light from nearby sources". If old light is traveling through expanding space toward us, it will record the expansion it experiences as it goes (in the frequency shift). If a light was emitted 10 Billion years ago and began its journey towards us through a non-accelerating expansion, then during this time the light should reflect a non-expanding, "linear", relationship of distance to red-shift" (Hubble Law). But, at the 5 Billion year point in expansion, this same light suddenly began to experience an accelerating expansion. Now we have a mix of linear and acceleration in the history of this light beam. But, at that point, it is much "closer" to us. In fact, by your offering, too close for acceleration red-shifting to significantly show up ("For small times the main effect is going to be linear."). The time that the old light traveled through, and experienced, accelerating expansion is equal to the time the new light traveled, which for the new light was too small for the acceleration to alter it from linear. So, if the old light was linear up until it began to experience acceleration, but the time it experienced acceleration was too short to alter it from linear, how then is it not linear?
It still looks like, to me, that this observation suggests the old light experienced acceleration from the beginning. In fact, if the acceleration shift added to the light doesn't happen long enough to show up in measurements, then all of this might suggest that acceleration has been going on all along, it's just that acceleration over the last 5 billion years is not going to show up, old or new.

Is this statement in Wikipedia correct, that in observations the new light is linear but the old is not?

 

[Ibix]

You misunderstand.

We cannot detect any cosmological redshift at all from very nearby sources. This isn't necessarily because it isn't happening, but because it's lost in all the sources of noise - thermal broadening, detector noise, Doppler from stellar and galactic motion, everything like that makes it impossible to see.

If you let light travel for further, though, the redshift builds up to where we can detect it. But the point Orodruin made formally, and I made less formally, is that whatever the expansion history of the universe the smallest deviation you can ever see from a flat line (no redshift with distance) is a sloped line (linear redshift with distance). Only if you let light travel further still will you be able to see that the relationship isn't linear.

If you want to see this in action, get Excel and plot $y=x^2$ for x in the range 0 to 10. Fix the vertical axis and then decrease the range of x to 0 to 5, then 0 to 1, then 0 to 0.5 then 0 to 0.1. At some point the line you know is curved will be indistinguishable from a straight line. The same is happening in the cosmological case - if you try to plot redshift versus distance you may know from cosmological models that the line should be curved, but you can't see the deviation from a straight line.

It's more than possible that, if we went back in time a few billion years and measured redshift versus distance, the line we plotted would be even more very nearly straight than the modern case. I don't know - I'd need to work through what the models say. But the recent history (whatever "recent" means to the person/alien drawing the graph) will always be close to linear.

 

[Rodney-Believes]

Thank you. But now I am struggling with when to apply d=Hv. What distance range does this hold up? If not all, why call it a Law? It sounds like that for very great distances it is useless. For close range, it is useless.

 

[Ibix]

For close range it doesn't work because the random velocity variation of galaxies is larger. I gather that the expansion-induced recession becomes dominant over that at about a hundred million light years. Your Wikipedia article says it fails at distances above about 1.4 billion light years such that light has been traveling for about 1.4 billion years (ignore the struck out bit - I forgot to account for expansion, ironically enough).

As to why it's called a law, I guess Hubble called it a law. I don't think law has a precisely defined meaning here. And it would be very far from the only thing called a law that is only accurate over a limited range (pretty much every thing Newton called a law, for example). That's one reason, I think, why modern theories like relativity and QM don't have many things called "laws".

 

[Rodney-Believes]

For that matter, the Hubble Value likely is decreasing so slowly it could take hundreds or thousands of years to measure it. What if G is not a constant, changing likewise so slowly it could take thousands of years for us to see it? You know, if gravity propagates at the speed of light, maybe the massive size of a black hole could be an indication of it. The outer stars would be feeling the gravity of the black hole that was generated thousands of years ago, when G was bigger. The inner stars would be experiencing the current G.

It blows the mind...

 

[PeterDonis]

You know, if gravity propagates at the speed of light, maybe the massive size of a black hole could be an indication of it. The outer stars would be feeling the gravity of the black hole that was generated thousands of years ago, when G was bigger. The inner stars would be experiencing the current G.

Please review the PF rules on personal speculation.

 

[Ibix]

For that matter, the Hubble Value likely is decreasing so slowly it could take hundreds or thousands of years to measure it.

I think you can see how the Hubble "constant" changed with time fairly easily from the existing data. It's related to the slope of the redshift-versus-distance graph.

 

[Arman777]

For the math of the of the Hubble Law

The proper distance is defined as,

$$d_p=c\int dt/a(t)$$ by using taylor approximation on $1/a(t)$ and by some other substitutions we get

$$d_p≈\frac{c}{H_0}z[1-\frac{1+q_0}{2}z]$$

So for $z<<2/(1+q_0)$ we have the Hubble Law.

Here $$q_0=1/2\Omega_m+\Omega_r-\Omega_{\Lambda}≈-0.55$$

 

[Rodney-Believes]

I think you can see how the Hubble "constant" changed with time fairly easily from the existing data. It's related to the slope of the redshift-versus-distance graph.

I read that one confirmation of Hubble Law is that you can determine the distance to an object (that I assume is linear) and divide it by the relative velocity measured to get the age of the universe. How long it would take them to come back together.

That implies that cosmology holds everything started out at a central point and that every object has been moving away from each other ever since (due to expansion). So, even for objects closer to us, (just moving away from us slower than distant objects and for which Hubble Motion is discernable) this implies expansion motion is simple drifting apart at a steady velocity (in order for the measured velocity divided by the measured distance to yield the age of the universe). So, if there is an acceleration in any part of the history of expansion, in the time any two objects have moved apart due to expansion, then this method of testing it against the known age of the universe might not work, or if it yields the current age it might call into question acceleration. If two objects, even relatively close, have been drifting apart due to expansion since the beginning (simply speaking), then any change in the rate of expansion would be part of the history that separation. Any acceleration observed anywhere would be part of the history of all separations due to expansion. Even if acceleration is small between close objects, with the universe accelerating for the last 5 billion years, this would add up. Can a moderately distant object still yield the age of the universe having acceleration a part of its expansion for the last 5 billion years? Am I making sense?

You are so kind and patient to help me. I appreciate it so much!

 

[PeterDonis]

I read

Where? Please give a specific reference.

 

[Rodney-Believes]

Please review the PF rules on personal speculation.

I'm sorry. I guess I don't understand the difference between scientific exploration and person ideas. Ibix prompted we me to wonder about constants. I googled constants, and found that some scientist wondered about G being a constant, set up experiments, and in addition examined measurements that went back 20 years. In their experiments, they did detect some fluctuations of G that suggested its value could be somehow influenced by the positions of our sun and planets. But, they did not suggest yet that G might not be constant. They did however offer the 20 year consistent number as comfort that it is. That got me thinking. If G is not a constant it could take hundreds or thousands of years for us to measure it, like the Hubble Value. I wondered how we could test G better. It is so weak that I wondered how to magnify it so we could examine it easier (when something is very small, magnify it to see). To do that, you'd need something very massive that would make gravity strong, and easier to see fluctuations, even small ones.. The problem is, even so, if G is change of thousands of years you'd still have a problem. That made me think about black holes, and millions of stars circling them, and galaxies millions of light years across. From that, I posted my idea to use a black hole and galaxies to wonder about G. I don't believe G is constant or not.

I just want you to understand, I didn't post that as an idea about gravity, just a wondering about how we could test G as a constant. It's hard to know when you cross the line verses thinking outside the box. I am very grateful for the willingness to help and don't want to offend anyone.

 

[PeterDonis]

I guess I don't understand the difference between scientific exploration and person ideas.

That's why we have rules to explain what we mean in the PF context. They are here:

https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/

In particular, see this part:

• Non-mainstream theories:
  Generally, in the forums we do not allow the following:
  • Discussion of theories that appear only on personal web sites, self-published books, etc.
  • Challenges to mainstream theories (relativity, the Big Bang, etc.) that go beyond current professional discussion
  • Attempts to promote or resuscitate theories that have been discredited or superseded (e.g. Lorentz ether theory); this does not exclude discussion of those theories in a purely historical context
  • Personal theories or speculations that go beyond or counter to generally-accepted science
  • Mixing science and religion, e.g. using religious doctrines in support of scientific arguments or vice versa.
  • Philosophical discussions are permitted only at the discretion of the mentors and may be deleted or closed without warning or appeal

I've italicized the bullet that's most applicable to the part of your previous post that I quoted. If your post had just stopped before that (i.e., just ended with the "what if G is not constant" sentence, nothing after it), it would have been fine; there is plenty of mainstream literature investigating the possibility that G might not be constant and exploring the implications. But the rest of your post was your personal speculation, based on your personal (mistaken) understanding.

I googled constants, and found that some scientist wondered about G being a constant, set up experiments, and in addition examined measurements that went back 20 years.

So why didn't you cite this reference?

I wondered how we could test G better.

No, you didn't. You might think you did, but you didn't. What you did was to speculate based on your mistaken understanding. What you should have done was cite the mainstream references you found, and ask about their implications if you thought that would be helpful. If you were wondering how we could test whether G has changed over longer periods of time, you should have gone looking for more mainstream literature addressing that question. Or asked here if anyone else could give any references to such literature.

It is so weak that I wondered how to magnify it so we could examine it easier (when something is very small, magnify it to see). To do that, you'd need something very massive that would make gravity strong

"Making gravity strong" has nothing to do with "magnifying" G. G is the same inside a black hole as it is anywhere else. This is an example of your mistaken understanding.

Yes, I know you didn't know this understanding was mistaken when you posted it. But that's why we emphasize that you should be looking at the mainstream literature. You can't even speculate usefully if you don't know what we already know and what other people have already tried.

 

[PeterDonis]

It's hard to know when you cross the line verses thinking outside the box.

Another thing to bear in mind is that PF is not intended for original research. It is intended for helping people to understand the current mainstream research that has already been done. So if you find yourself, for example, thinking up ways of your own to test whether G is constant, instead of looking for research that has already been done to test whether G is constant, you're probably crossing the line.

 

[Rodney-Believes]

Another thing to bear in mind is that PF is not intended for original research. It is intended for helping people to understand the current mainstream research that has already been done. So if you find yourself, for example, thinking up ways of your own to test whether G is constant, instead of looking for research that has already been done to test whether G is constant, you're probably crossing the line.

Got it. I will be more careful. No desire to offend anyone.

 

[Bandersnatch]

So, if there is an acceleration in any part of the history of expansion, in the time any two objects have moved apart due to expansion, then this method of testing it against the known age of the universe might not work, or if it yields the current age it might call into question acceleration.

The thing is, for the first half-ish of the history of the universe, there was deceleration. Acceleration has been happening during the other half or so. So you have a curve that slopes one way for about half its length, and then the other way. This makes using a straight line approximation kinda-sorta give the correct age:

This graph shows how all distances have changed over time, growing from 0 to their current size (i.e. scale factor = 1). You can see that it took almost 14 billion years for any distance to grow to the current size. The curve sloping downwards at the beginning is deceleration. The later acceleration is less pronounced, but it's there.
You can perhaps see how you could just about replace this curve with a straight line starting at the now point (13.8, 1) and initially tangent to the first bit of the curve, and not get that much of a different result as to where it crosses the x axis.

 

[Rodney-Believes]

The thing is, for the first half-ish of the history of the universe, there was deceleration. Acceleration has been happening during the other half or so. So you have a curve that slopes one way for about half its length, and then the other way. This makes using a straight line approximation kinda-sorta give the correct age:
View attachment 239156
This graph shows how all distances have changed over time, growing from 0 to their current size (i.e. scale factor = 1). You can see that it took almost 14 billion years for any distance to grow to the current size. The curve sloping downwards at the beginning is deceleration. The later acceleration is less pronounced, but it's there.
You can perhaps see how you could just about replace this curve with a straight line starting at the now point (13.8, 1) and initially tangent to the first bit of the curve, and not get that much of a different result as to where it crosses the x axis.

Thanks Bandersnatch! I have an expansion motion simulator and I was able to generate a chart from the perspective of the observer that looks a lot like this graph (I have to set the observer out of sync with the Hubble flow to cause it). I plan to play with it some more to help me understand. I would post the chart here but I don't want to get band.

Thanks again.

 

[Bandersnatch]

I have an expansion motion simulator

Oh, neat. Can you give us a link?
(not sure why you'd be worried about bans)

 

[Rodney-Believes]

Oh, neat. Can you give us a link?
(not sure why you'd be worried about bans)

The simulator was written by me and therefore it is "Personal Theory". I am a data analyst by trade and an applications developer. The motion that this simulator is using to generate observations is steady rate moving away from a central point. That is not mainstream established physics. I've been advised to keep such things to myself while on this site.

 

[PeterDonis]

Can you give us a link?
(not sure why you'd be worried about bans)

As you see, @Rodney-Believes does have a good reason for not posting the link in a public thread (see posts #17 and #18 for more background). Sending it via PM would be fine.