Measuring Redshift to Support Accelerating Universe

[azerbajdzan]

Universe appears to be expanding at an increasing rate.
What measurements were performed to support this idea?

My current understanding is that in general redshift of distant stars/galaxies is increasing with time.

So to me the measurements may look like this:
We choose one star, measure its redshift, say it would be 1 Hz.
Then one year later we measure the redshift of the same star and it would be, say, 2 Hz.
We perform the same measurements on many stars and if most of them have increased their redshift it suggest that in general the universe expansion increases.

Is it so or my understanding is not correct?

 

[phinds]

The redshift measurements are taken on numerous stars over a wide range of distances.

Redshift is not the only evidence for acceleration. The topic is discussed here VERY frequently. Do a forum search for (for example) "evidence for accelerating universe"

 

[azerbajdzan]

To me the redshift at particular time only means that universe is expanding not that it is expanding at increasing rate.
The evidence of accelerating expanding would be if redshift increases with time. But it looks to me that the difference between redshift in, say, 2012 and in 2013 do not differ to much for it to be measurable. Or is it measurable?

What is other evidence of acceleration?

 

[phinds]

To me the redshift at particular time only means that universe is expanding not that it is expanding at increasing rate.
The evidence of accelerating expanding would be if redshift increases with time. But it looks to me that the difference between redshift in, say, 2012 and in 2013 do not differ to much for it to be measurable. Or is it measurable?

You are completely missing the point. Taking red-shift measurements at different distance is taking them at different times. The light from a galaxy 1 billion light years away was emitted 1 billion years ago. The light from a galaxy 10 billion light years away was emitted 10 billion years ago.

What is other evidence of acceleration?

Which part of Do a forum search for (for example) "evidence for accelerating universe" did you not understand ?

 

[Mordred]

As Phinds pointed out we do not rely on one method.

this article covers some of the methods involved.

https://www.physicsforums.com/showpost.php?p=4447058&postcount=6

my signature has links with further information. I recommend "Expanding confusion" by Lineweaver and Davies found under the cosmology101 link of my signature. The cosmocalc is also a handy tool to understanding.

 

[Landrew]

Is it really accelerating, or is that how it would appear when you are looking over a vast expanse of expanding space? Since space itself is expanding, it stands to reason that the longer your perspective across it, the more rapidly it would appear to be expanding.

Objects are not really moving away from each other of course, the space between them itself is growing larger. This in itself presents a strange problem. If the Earth exists in a narrow "Goldielocks Zone" in it's orbit around the sun, where life could not exist were it much nearer or much farther from the sun. If fossil evidence suggests that life has existed on Earth for several billion years, how did the Earth manage to stay within the narrow "zone of life" for all that time? Would not the expansion of space have caused a decrease in solar radiation reaching the planet? What are the explanations for this?

 

[Mordred]

The articles I posted cover that, expansion doesn't occur in gravitationally bound regions. Instead it only occurs between galaxies that are not gravitationally bound. Its not acceleration as per se there is no inertia. As you say its simply the amount of space increasing.

 

[azerbajdzan]

Which part of Do a forum search for (for example) "evidence for accelerating universe" did you not understand ?

I understand it... and I read many articles about it... on wikipedia and others. But this is question that I still do not understand, that is why I am asking.

Taking red-shift measurements at different distance is taking them at different times.

I understand this. But then they say, that more distant objects have bigger redshifts. More distant means more back in time. So I explain it the opposite way... the more back in the time the more the red shift is the bigger the expansion was... i.e. the universe expansion is decreasing.

That is my logic... I sure that I misunderstood something... and asking where I made a mistake...

 

[Mordred]

perhaps this tool will help, lightcone calculator first link of my signature. I chose a 30 step and column selection of the values I wish to see. The calc has other selections I chose to turn off.

From this you can the redshift vs time aspect to distance relation, the calculator can also graph the results but due to scale of this calculation it wouldn't show much without rescaling vertical and horizontal values. the thread at the top has numerous examples some showing the graph for a better visualization.

https://www.physicsforums.com/showthread.php?t=634757

$${\small\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.92&0.693&0.307\\ \hline \end{array}}$$ $${\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline S&a=1/S&z&T (Gy)&R (Gly)&D (Gly)&D_{then}(Gly)&a'R_{0} (c) \\ \hline 1090.000&0.000&1089.000&0.0004&0.0006&45.332&0.042&21.02\\ \hline 739.062&0.001&738.062&0.0007&0.0012&45.031&0.061&16.62\\ \hline 501.112&0.002&500.112&0.0013&0.0022&44.654&0.089&13.29\\ \hline 339.773&0.003&338.773&0.0025&0.0040&44.184&0.130&10.71\\ \hline 230.379&0.004&229.379&0.0046&0.0072&43.602&0.189&8.69\\ \hline 156.206&0.006&155.206&0.0084&0.0130&42.888&0.275&7.08\\ \hline 105.913&0.009&104.913&0.0153&0.0235&42.012&0.397&5.79\\ \hline 71.813&0.014&70.813&0.0277&0.0423&40.943&0.570&4.75\\ \hline 48.692&0.021&47.692&0.0501&0.0759&39.639&0.814&3.89\\ \hline 33.015&0.030&32.015&0.0902&0.1363&38.052&1.153&3.20\\ \hline 22.386&0.045&21.386&0.1621&0.2445&36.120&1.614&2.63\\ \hline 15.178&0.066&14.178&0.2911&0.4383&33.771&2.225&2.16\\ \hline 10.291&0.097&9.291&0.5223&0.7851&30.918&3.004&1.78\\ \hline 6.978&0.143&5.978&0.9361&1.4037&27.455&3.935&1.47\\ \hline 4.731&0.211&3.731&1.6741&2.4969&23.266&4.918&1.22\\ \hline 3.208&0.312&2.208&2.9777&4.3736&18.248&5.688&1.03\\ \hline 2.175&0.460&1.175&5.2154&7.3341&12.398&5.700&0.90\\ \hline 1.475&0.678&0.475&8.7894&11.1153&6.042&4.097&0.88\\ \hline 1.000&1.000&0.000&13.7872&14.3999&0.000&0.000&1.00\\ \hline 0.681&1.468&-0.319&19.7042&16.2016&4.910&7.207&1.30\\ \hline 0.464&2.154&-0.536&26.0846&16.9288&8.515&18.346&1.83\\ \hline 0.316&3.162&-0.684&32.6380&17.1800&11.040&34.912&2.65\\ \hline 0.215&4.642&-0.785&39.2497&17.2617&12.776&59.303&3.87\\ \hline 0.147&6.813&-0.853&45.8801&17.2877&13.963&95.126&5.67\\ \hline 0.100&10.000&-0.900&52.5163&17.2961&14.772&147.715&8.33\\ \hline 0.068&14.678&-0.932&59.1545&17.2987&15.323&224.908&12.22\\ \hline 0.046&21.544&-0.954&65.7934&17.2994&15.698&338.212&17.93\\ \hline 0.032&31.623&-0.968&72.4323&17.2998&15.954&504.520&26.32\\ \hline 0.022&46.416&-0.978&79.0713&17.2998&16.129&748.627&38.64\\ \hline 0.015&68.129&-0.985&85.7103&17.3000&16.247&1106.926&56.71\\ \hline 0.010&100.000&-0.990&92.3494&17.2999&16.328&1632.838&83.24\\ \hline \end{array}}$$

 

[jackmell]

Why isn't anyone mentioning the supernova data to support accelerated expansion?

 

[phinds]

I understand this. But then they say, that more distant objects have bigger redshifts. More distant means more back in time. So I explain it the opposite way... the more back in the time the more the red shift is the bigger the expansion was... i.e. the universe expansion is decreasing

You have a LOT of company in thinking that --- it seems to be the first thought of a great many people when first looking at it and it DOES seem reasonable at first. I think Mordred's post will help you understand.

 

[Mordred]

it is mentioned the cosmic distance scale of the first article I linked

https://www.physicsforums.com/showpost.php?p=4447058&postcount=6 see the bottom section of that article.

here is a cut and paste from it

Cosmic Distance ladder, also known as Extragalactic distance scale. Is easily thought of as a series of different measurement methods for specific distance scales. Previous in the article we discussed the various forms of Redshift. These principles are used in conjunction with the following methods described below. Modern equipment now allows use spectrometry. Spectrographs of an element give off a definite spectrum of light or wavelengths. By examining changes in this spectrum and other electromagnetic frequencies with the various forms of shifts caused by relative motion, gravitational effects and expansion. We can now judge an objects luminosity where absolute luminosity is the amount of energy emitted per second.

Luminosity is often measured in flux where flux is

$$f=\frac{L}{4\pi r^2}$$

However cosmologists typically use a scale called magnitudes. The magnitude scale has been developed so that a 5 magnitude change corresponds to a differents of 100 flux.
Rather than cover a large range of those distance scales or rungs on the ladder I will cover a few of the essential steps to cosmological distance scales. The first rung on the ladder is naturally.

Direct measurements: Direct measurements form the fundamental distance scale. Units such as the distance from Earth to the sun that are used to develop a fundamental unit called astronomical unit or AU. During the orbit around the sun we can take a variety of measurements such as Doppler shifts to use as a calibration for the AU unit. This Unit is also derived by a method called Parallax.

Parallax. Parallax is essentially trigonometric measurements of a nearby object in space. When our orbit forms a right angle triangle to us and the object to be measured
With the standardized AU unit we can take two AU to form the short leg. With the Sun at a right angle to us the distance to the object to be measured is the long leg of the triangle.

Moving Cluster Parallax is a technique where the motions of individual stars in a nearby star cluster can be used to find the distance to the cluster.

Stellar parallax is the effect of parallax on distant stars . It is parallax on an interstellar scale, and allows us to set a standard for the parsec.

Standard candles A common misconception of standard candles is that only type 1A supernova are used. Indeed any known fundamental distance measurement or stellar object whose luminosity or brightness is known can be used as a standard candle. By comparing an objects luminosity to the observed brightness we can calculate the distance to an object using the inverse square law. Standard candles include any object of known luminosity, such as Cepheid’s, novae, Type 1A supernova and galaxy clusters.

 

[Mordred]

just as side note, on the accelerating expansion rate let's take a simple math expression

x=x+expansion%. set x= distance

start with x=1 and for simplicity use 100% for expansion.

its easy to see why its considered an accelerating expansion.

 

[Lino]

... the more back in the time the more the red shift is the bigger the expansion was...

azerbajdzan, The key thing that red-shift shows us is that the speed at which an object moves away from us is proportional to its distance from us - it doesn't have to be accelerating faster. Think of a car moving away from you (or traffic lights), it is going 10mph after 1 second, 20mph after 2 seconds, 30mhp after 3 seconds, ... - its speed is getting bigger not its rate of acceleration - the acceleration is constant. The same applies to the stars / galaxies moving away from us - the further from us that they are, the faster they are moving, the greater their redshift - even if their acceleration is constant.

And you're right, if we could measure the change in the red-shift from year to year, we would see it growing. However, the rate of expansion is only (approximately) 1/144% per billion years and (at present) we can't measure red-shift that accurately. That's why, as phinds mentioned we do lots (and lots) of measure at lots of different distances, which equates to doing measures billions of years apart and shows us the different values for red-shift. And yes, the rate of acceleration was less for those more distant objects (because we are looking back in time), but only by relatively small amounts. In terms of understanding red-shift, you can ignore this small part initially.

If you want to know more about the changing rate of acceleration due to expansion, there are special objects (a specifc type of supernovea as jackmell mentioned) that do allow us to gather even more information because we know more about them, and it is these and other evidence that shows us that the rate of acceleration is growing and not just the speed. You probably know that red-shift was identified in the 1950's by a guy called Hubble, but you might not be aware that it was only (approximately) 10 years ago that a guy called Perlmutter (and others) identified the changing / increasing rate of acceleration. If you do the search that phinds suggested, you will find plenty of material related to this.

 

[George Jones]

And you're right, if we could measure the change in the red-shift from year to year, we would see it growing.

Not for all objects.

As Aimless said, observation time have been too short to see redshift change. We are close to being able to do this, but, for economic and other reasons, such a project won't start for several decades. Once started, the project would take a couple of decades to start to get good results. See

http://arxiv.org/abs/0802.1532

Also, redshifts don't necessarily increase with time. Figure 1 from this paper plots redshift versus time. The three red curves are for objects in our universe. As we watch (over many years) a distant, high redshift object, A, we will see the object's redshift decrease, reach a minimum, and then increase. If we watch a much closer, lower redshift object, B, we see the object's redshift only increase.

Roughly, when light left A, the universe was in a decelerating matter-dominated phase, and when light left B, the universe was in the accelerating dark energy-dominated phase.

 

[Lino]

Not for all objects.

Thanks for reminding me of this George, very much appreciated. Would you think that the OP should ignore this for the moment and focus on getting to grips with basic (I don't know what other word to use) red-shift first?

 

[azerbajdzan]

All current observations are for me not enough convincing to say that universe is expanding at increasing rate. And then think up some dark matter and dark energy to support this idea. More likely it is that there is no dark matter (except black holes, faint stars and similar common objects) and no dark energy... but that we do not explain what we see by observation correctly and that another "Einstein" is needed to explain why it is so without using any "dark energy" in the theory.

Do not understand it that I am presenting myself in the position that I am able to explain these things correctly.
No, I have no idea too. I am just skeptical about current explanations using "dark energy".

 

[phinds]

All current observations are for me not enough convincing to say that universe is expanding at increasing rate.

Well, good luck with that.

And then think up some dark matter and dark energy to support this idea.

Again, you misunderstand completely. Dark matter has nothing to do with expansion.

More likely it is that there is no dark matter (except black holes, faint stars and similar common objects)

No, none of those can possibly be dark matter. You clearly do not understand the characteristics of dark matter.Your problem throughout seems to be that for both dark energy and dark matter (which have NOTHING to do with each other) you are simply ignoring the direct results of empirical observations.

 

[azerbajdzan]

I have not said that dark matter has something to do with expansion.
It is dark energy that causes expansion by today's physics.
I just mention dark energy and dark matter together as an examples that when people are not able to explain something then they invent some terms/ideas to support the theory. But the reality could be that there is nothing such as dark energy or dark matter and that it is only the incomplete theory.

Maybe today's theory needs the same step forward like it was step from Newton to Einstein. So maybe another "Einstein" in the future would be able to explain what we see by theory where there would not be any dark energy or dark matter.

 

[WannabeNewton]

This thread has derailed into nonsense to be honest. There is a wealth of information on dark energy that you can read up on through the internet; you should do so before making grandoise claims about its non-existence/invalidity.

 

[azerbajdzan]

Many prominent physicists admit that it is possible that "dark energy theories" could be wrong, although for now it is the most satisfying theory. (Like Newton's theory was/is imprecise in some situations, so in strict sense it was/is wrong in general)

Example:
Perihelion precession of Mercury... if there were no Einstein some physicist could make up, say, "transparent energy" as an explanation why perihelion precession of Mercury does not comply with Newtonian mechanics. This theory could describe observation of Mercury precisely using some properties of hypothetical "transparent energy". But then there would come Einstein and would say... there is no need for "transparent energy", look, here is my General Theory of Relativity which explains the situation with Mercury and it does not need any existence of "transparent energy" and in fact no "transparent energy" exists.

The same can happen with "dark energy".

 

[mfb]

Physical models are always "the best thing we know today to explain observations".
Those observations are sometimes model-dependent, sometimes not.

I understand this. But then they say, that more distant objects have bigger redshifts.

No. Compared to simple extrapolation based on the current expansion rate, they have less redshift. Which means expansion was slower in the past.

 

[azerbajdzan]

"Quote by azerbajdzan
I understand this. But then they say, that more distant objects have bigger redshifts."

No. Compared to simple extrapolation based on the current expansion rate, they have less redshift. Which means expansion was slower in the past.

So bigger or less? Your post confused me even more.

This is quote from this link http://www.setterfield.org/000docs/redshift.htm :
"Edwin Hubble showed in 1929 that the more distant the galaxy, the larger this "redshift"."
So it is like I said according to this article.

 

[marcus]

I have not said that dark matter has something to do with expansion.
It is dark energy that causes expansion by today's physics.
I just mention dark energy and dark matter together as an examples that when people are not able to explain something then they invent some terms/ideas to support the theory. But the reality could be that there is nothing such as dark energy or dark matter and that it is only the incomplete theory...

There is some truth in what you say. I'm sleepy now and can't talk. Please check back here in 10 or 12 hours, give me time to get some sleep. We may find some things we can agree on.

Also part of the confusion has to do with imprecision of language. Often, in English, when someone says "growth rate" they mean the PERCENTAGE rate of increase. Like 2% increase per year. But "rate" can also mean actual SPEED. It's different.

A distance, say the height of a tree, can increase at a CONSTANT (percentage) rate and increase at a faster and faster speed. It can even grow at a gradually DECLINING (percentage) rate and still grow at an increasing speed (measured in centimeters per year).

So that is a problem with ordinary common spoken language. It is not as clear as mathematics. You need to be more clear about what you mean by "acceleration", and what you think other people mean by "acceleration".

The current rate of distance expansion in the universe is 1/144% per million years, according to latest measurment. This is believed to be decreasing and it is expected to continue decreasing in the foreseeable future. According to standard cosmic model it will decrease to 1/173% per million years in the very long term.

This decrease in the expansion rate is so slow that if you could watch a particular large distance grow for a long time you would see it get bigger at an increasing speed.

If you are interested in getting clear about cosmic expansion and what people mean by "acceleration" in this context, please give me a chance to get some sleep and check in here later.

I think you are right to be skeptical about "dark energy". The effect might not be caused by an actual "energy" but simply by a constant term in the equation that governs cosmological distances. It has not been proven that it is due to any actual energy.

 

[mfb]

So bigger or less? Your post confused me even more.

This is quote from this link http://www.setterfield.org/000docs/redshift.htm :
"Edwin Hubble showed in 1929 that the more distant the galaxy, the larger this "redshift"."
So it is like I said according to this article.

For more distant galaxies, the redshift is larger - this just means that the universe expanded all the time.
For more distant galaxies, the redshift is not as large as you would expect for a constant expansion - this effect is way smaller than the first one, and it corresponds to the acceleration of the expansion.

 

[marcus]

Azer,
I don't know if you still have questions or are confused. MFB answered with the right information but you may not have understood.
If you still want to discuss, please continue. I will try to help too.

In the meantime there is a way to get a TABLE of the HISTORY of the expansion speed (as a multiple of the speed of light) of a sample distance, namely the distance that right now today is expanding at the speed of light---this is 14.4 billion ly. The other distances are expanding proportionally,with speeds proportional to their size. So this tells a typical expansion speed history.

Just go here:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
Change the number of steps from 10 to 46 (or 47 or 48, we need more steps to see the speed clearly reach its minimum and start increasing).

Then, before you press "calculate", click on "open column definition and selection" and select
"a'R₀(history)" this is the speed of expansion of that representative sample distance.
You click on the X in that box and it changes to a check "√ "
This means that the speed history will show up in the table.

Now press "calculate".

You will see that the speed that particular distance was expanding started out very fast (like 21c) and declined for the first 7.6 billion years. And then around year 7.6 billion it reached a minimum speed of about 0.82 c. And then the speed started to increase. So that is when "acceleration" began.

However all during the past and also into the foreseeable future the PERCENTAGE distance growth rate is decreasing. As I said it is now estimated at 1/144% per million years and in long term future will settle down towards 1/173% per million years.
===================

You can use this table calculator to experiment with what distance growth would have looked like with ZERO COSMOLOGICAL CONSTANT or (if you like to say it) no "dark energy". If you want to do that you can ask, or you can go up to the top of the page where you see 17.3 in a box and change that to some much larger number, like 173 or1730, and then press calculate again. Then the speed will not bottom out and start increasing. It will keep on decreasing up to now and on into future.

 

[azerbajdzan]

Thank you for your comment. I have got some questions.

What is D_now, D_then, D_hor? I can not see a definition of it on that page. I guess diameter of universe? If so what is meant by "then" (when then?), "hor", what is meant by "now"? There is only one "now", bu in the table there is one "now" in each row. So when now?

What is v_now, v_then? I know it is a speed... but speed of what and "when then" and "when now"? Again definition of both is missing on the page.

 

[Dale]

Closed pending moderation.

EDIT: The thread is re opened. I remind the participants to keep the discussion within the bounds of the forum rules:
https://www.physicsforums.com/showthread.php?t=414380

Dark energy and accelerating expansion are both part of the current mainstream scientific literature. Any objections to them on this forum must also be part of the current mainstream scientific literature.

 

[marcus]

Thank you for your comment. I have got some questions.

What is D_now, D_then, D_hor? I can not see a definition of it on that page. I guess diameter of universe? If so what is meant by "then" (when then?), "hor", what is meant by "now"? There is only one "now", bu in the table there is one "now" in each row. So when now?

What is v_now, v_then? I know it is a speed... but speed of what and "when then" and "when now"? Again definition of both is missing on the page.

Hi Azer, sorry I had a lot of work to do yesterday and didn't have time to look at PF Cosmo, so did not see your post. I am glad you are still interested in "acceleration" question.

But you also ask too many other questions here for me to try to answer in this thread !

When you have the table-calculator on your screen, try moving the pointer over the blue dots. This will bring pop-up definitions of things like Dnow and Dthen.

Also here is a user guide: http://cosmocalc.wikidot.com/lightcone-userguide.

An aerospace engineer who is a PF member made this cosmology table-calculator. I think it is very good. But it has a great deal of different kinds of information.

Let's get back to talking simply about the two different measures of expansion:
(percentage) RATE and, on the other hand, expansion SPEED of a sample distance that we choose to watch.

I will use "column definition and selection" to make the other columns go away, so we can focus on only the relevant columns.

 

[marcus]

This time I made the table have only 18 steps, to make it small enough for me to read easily. And using "column definition and selection" I reduced the number of decimal places in some of the columns to make the numbers easier for me to read.

The table says that in year 545 million the expansion RATE was 1/8% per million years.

But by year 801 million the rate had already declined to 1/12% per million years.

Do you see how you can read the R column to tell the percentage rate of expansion of distances?

You can see that today, which is year 13.787 billion, cosmological distances are growing at rate of 1/144% per million years. And the cosmological constant sets a lower bound on how small the rate can get. According to latest measurement of cosmological constant, the lower bound on the rate is 1/173% per million years. I think you can see this in table.

$${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&T (Gy)&R (Gly)&a'R_{0} (c) \\ \hline 0.10&0.545&0.8&1.76\\ \hline 0.13&0.801&1.2&1.55\\ \hline 0.17&1.175&1.8&1.37\\ \hline 0.22&1.723&2.6&1.21\\ \hline 0.28&2.519&3.7&1.08\\ \hline 0.36&3.666&5.3&0.97\\ \hline 0.46&5.286&7.4&0.90\\ \hline 0.60&7.496&9.9&0.87\\ \hline 0.77&10.349&12.4&0.90\\ \hline 1.00&13.787&14.4&1.00\\ \hline 1.29&17.659&15.8&1.18\\ \hline 1.67&21.799&16.5&1.45\\ \hline 2.15&26.085&16.9&1.83\\ \hline 2.78&30.444&17.1&2.34\\ \hline 3.59&34.838&17.2&3.01\\ \hline 4.64&39.250&17.3&3.87\\ \hline 5.99&43.669&17.3&5.00\\ \hline 7.74&48.092&17.3&6.45\\ \hline 10.00&52.516&17.3&8.33\\ \hline \end{array}}$$

Now let's talk about SPEED of growth of a sample distance that we choose to follow. The "a" in the first column is called the "scale factor" and it tells the RELATIVE SIZE of distances. In year 545 million they were one tenth (0.1) what they are today. In year 52.5 billion (the bottom row of table) they will be ten times what they are today. You surely see that.

Now we take as a SAMPLE distance one whose SIZE TODAY = 14.4 billion light years. So back in year 545 million its size was 1.44 billion light years. We are going to watch that distance grow and measure the SPEED.

The speed is in the right-most column, you can see that it does something very interesting. It declines at first until at around year 7.5 billion it is only 0.87c.

That is the slowest (87% of the speed of light) that particular distance ever grows. After that the speed picks up.

All cosmological distances (i.e. those between pairs of observers at CMB rest) grow proportionally to their size. A distance twice as big as our sample would grow at twice the speed. Or half as big would grow at half the speed.

All cosmological distances reach their slowest growth speed at around year 7.5 billion.

So the percentage RATE continues declining (eventually approaching its lower bound.)
But the speed of any sample distance that we choose to watch will begin to increase at around year 7.5 billion.

Now this increase depends on there being a lower bound on the percentage rate. That is governed by the cosmological constant. We can experiment with CHANGING the lower bound.
Instead of having it be 1/173% per million years, we can make it much smaller. Like 1/2000% per million years. This corresponds to assuming a much smaller cosmological constant.
We can do this by changing one of the numbers in a box at the top of the table-calculator page.
Instead of having 17.3 in the box, we could put 200, for example. By making cosmological constant very small, we can make the acceleration go away. But that is something to think about later.

The blue dots that give you explanations of the column quantities are in the menu you get when you click on "column definition and selection". If you explore with the calculator you will learn quite a bit of quantitative cosmology on your own strength, without help.