Measuring the Universe's expansion rate

[Cimion]

From our perspective the Universe is expanding faster the further away things get, correct? Given that we are measuring further and further back in time my question is this. If you were at the furthest known point in the Universe looking back at our galaxy and attempting to measure the expansion rate wouldn't time indicate the expansion rate was actually slowing down.

 

[Drakkith]

From our perspective the Universe is expanding faster the further away things get, correct?

Objects further away have higher recession velocities, but the rate of expansion remains the same.

If you were at the furthest known point in the Universe looking back at our galaxy and attempting to measure the expansion rate wouldn't time indicate the expansion rate was actually slowing down.

No, they would measure the exact same effects that we measure here.

 

[Arman777]

From our perspective the Universe is expanding faster the further away things get, correct? Given that we are measuring further and further back in time my question is this. If you were at the furthest known point in the Universe looking back at our galaxy and attempting to measure the expansion rate wouldn't time indicate the expansion rate was actually slowing down.

Further to the what @Drakkith said, The recession velocity is proportional to distance so we can write $V∝D$ (Or in an exact form we can write $V=HD$).

The important thing you should notice in here that $H$ (Hubble parameter or expansion rate) is actually a function of time and it can be written as $H(t)=\frac {\dot{a}(t)} {a(t)}$. In this case, wherever you go in space the expansion rate will be the same cause it's a time-dependent function, not a position dependent.

But further, as you already said Recession velocity ($V$) is a function of Distance.

Note that $H(t)$ also changes with time so in this sense, we can think $V$ is not only position dependent but also as a time-dependent factor. But the change in $H(t)$ will be really small.

 

[Hellmut1956]

My question is if we know the rate of change the causes have to the behaviour of the universe expansion. I know that my question consists of quite a number of "sub-questions" so I try to explain myself.

1. In the moment of the Big Bang the universe had the size of a "mathematical point" and then it started to expand.
1.1 There was an initial "speed" of how the universe expanded.

I do believe to understand that at this initial moment everything that makes up our universe already existed but in form of energy.
Was the "Plank length, 1,616199 * 10^-35 meter" and the "Plank time, 5,39106 * 10^-44 seconds" then shorter? Is the current stipulated size of both units "today" the result of the universe expansion? Will those units increase over time?

1.2 The "texture" of the universe to what I have understood is a matrix and that the expansion changes the "distance" between its nodes.

So my question involves the following. Does the universe at the "moment" of the Big Bang have an initial "speed" and
- did the gravity have the effect of slowing down this initial speed of expansion?
- did the "dark energy" then already impacted as an accelerating moment to the expansion rate that did "equal" the slowing effect of gravity approximately 5 billion years ago?

Can we identify how the effect of expansion rate of the universe was, is and will be in the future due to the 2 effects, gravity and dark energy impacting it?
Is it linear or is it another kind of rate change? I guess the impact on the rate of expansion of this 2 "forces" have to be identified individually, while we now the rate of the inverse square of the gravity. Can we get data from measurements today or are our tools still so inaccurate that we only can perceive the impact of the dark energy in distances greater than the size of clusters?

And finally my last question:
If the unit size of the Plank units for time and distance did change as a side effect of the universe expansion, do we have a clue as to when and how we can experimentally realize the size of this units in the past, today as specified above and in the future? I have read it could come the moment in a distant future where the "tissue" of the universe where the 2 plank units for time and distance get so "big in value" that the strong force would not be able to keep the subatomic parts of an atom glued together!

I do excuse myself to you readers. I did not have the ability to think in the language of mathematics when I decided to go for an engineering career ant not for physics. Since I finished my studies of mechanical engineering soon after I was promoted into managerial functions and did so not even practice my limited mathematical skills. So while I know I would be better of expressing my thoughts mathematically this is the best I can!

 

[Drakkith]

1. In the moment of the Big Bang the universe had the size of a "mathematical point" and then it started to expand.
1.1 There was an initial "speed" of how the universe expanded.

In an infinitely sized universe, the singularity occurred everywhere and not at a single point in space. As to the initial rate of expansion, I can't answer. It was certainly many many times greater than it is in the present, but I don't know how rapid it might have been.

Was the "Plank length, 1,616199 * 10^-35 meter" and the "Plank time, 5,39106 * 10^-44 seconds" then shorter? Is the current stipulated size of both units "today" the result of the universe expansion? Will those units increase over time?

Those units do not change over time.

- did the gravity have the effect of slowing down this initial speed of expansion?

Yes, gravity has acted to slow the expansion from the very beginning as far as we know. One of the main reasons that expansion is accelerating is that gravity drops off as objects recede from each other and the density of the universe decreases over time.

- did the "dark energy" then already impacted as an accelerating moment to the expansion rate that did "equal" the slowing effect of gravity approximately 5 billion years ago?

I'm sorry but I'm having difficulty understanding this question.

 

[Arman777]

In the moment of the Big Bang the universe had the size of a "mathematical point" and then it started to expand.

Describing "the singularity" as a "mathematical point" is not a good approach when we try to understand what really happened. When we try to explain "How the universe begin?" we should always use the "singularity" and try to avoid the term like "point".

1.1 There was an initial "speed" of how the universe expanded.

We know that in the cosmic inflation theory, SM (Standart Model) particles created after the inflation (by inflation). Hence we can say that in the inflation period the universe was de Sitter Universe, where $a(t)∝e^{Ht}$ (Not exactly like this but close to this). Now, Inflation happened and SM particles get created by inflation and then (since there are now matter and radiation) the universe starts to evolve in a different way, For example, In the early universe radiation will be dominated and the universe will evolve like $a(t)∝t^{\frac {1} {2}}$ after a time the effect of the radiation density to the expansion will be unimportant. Hence, the universe will evolve as a matter dominated case, which $a(t)∝t^{\frac {2} {3}}$.

-did the "dark energy" then already impacted as an accelerating moment to the expansion rate that did "equal" the slowing effect of gravity approximately 5 billion years ago?

I will separate your question into the two parts. First part is that the density of the cosmological constant doesn't change with time. It's a just a property of the cosmological constant.

The second part is about the Hubble Parameter, In the early universe as I said the density of the radiation had much more effect on the Hubble parameter. Why? Because the density of the Radiation goes by $a^{-4}$ while the matter is $a^{-3}$ and as I said the density of the cosmological constant doesn't change with time.

So let's make a chronological order,
After the inflation universe was radiation dominated, then it turned to be matter dominated, and in the future when the density of the matter gets really low, the universe will be Lambda-dominated. And scale factor will be proportional to the $e^{Ht}$ as I described above.

In this sense the answer to your question will be; Lambda was affecting the same because the density of the lambda doesn't change with time. But the expansion rate was a bit higher. Because for a matter dominated universe H goes like $\frac {2} {3t}$ so in the past H was a bit higher.

Can we identify how the effect of the expansion rate of the universe was, is and will be in the future due to the 2 effects, gravity and dark energy impacting it?

You can use the Friedmann Equation in this form.

$\frac {H^2} {(H_0)^2}=Ω_{0,R}a^{-4}+Ω_{0,M}a^{-3}+Ω_{0,κ}a^{-2}+Ω_{0,Λ}$

For a flat universe $Ω_{0,κ}=0$ and we can also assume $Ω_{0,R}=0$ (Since radiation density is only important in the early universe) then we have,

$\frac {H^2} {(H_0)^2}=+Ω_{0,M}a^{-3}+Ω_{0,Λ}$

You should take $a(t_0)=1$ so that the $a$ term in the equation will represent the past
For example 5 billion years ago, scale factor will be, $a(t)=0.625$
you can do this from here,

http://home.fnal.gov/~gnedin/cc/

 

[Bandersnatch]

So my question involves the following. Does the universe at the "moment" of the Big Bang have an initial "speed" and
- did the gravity have the effect of slowing down this initial speed of expansion?
- did the "dark energy" then already impacted as an accelerating moment to the expansion rate that did "equal" the slowing effect of gravity approximately 5 billion years ago?

If you look at distant objects in the universe today, every one of them, unless already gravitationally bound, will have some 'speed' (let's call it recession velocity). This recession velocity is being affected by retarding influence from the gravity of matter and radiation, and by accelerating influence from dark energy.
All of this you appear to already understand.

Now, instead of singling out some earlier moment in the expansion, and calling it big bang, and then wondering what was different back then, take your understanding of the current state and imagine you wind back the time. Best to pick some random distant galaxy and think about what happens to it w/r to us.

The recession velocity of that galaxy will for a while decrease as you roll back the time and it gets closer (the dark energy dominated era), before gravity becoming strong enough to dominate. From that point onward, the recession velocity of that galaxy will increase towards the past, and keep doing so indefinitely (well, until you roll back the time sufficiently for it to be on top of you).

You can extrapolate it like that all the way back to the big bang singularity, and at no time will the influences of neither gravity nor the dark energy stop affecting the galaxy.

This behaviour is really no different than the behaviour of a body moving under the influence of two opposing forces with different dependence on distance. Like a rocket with a weak engine with infinite fuel and some initial velocity trying to take off from a planet - only every pair of two points in the universe see each other as such rockets.

Can we identify how the effect of expansion rate of the universe was, is and will be in the future due to the 2 effects, gravity and dark energy impacting it?

That's the essence of what the Friedmann equations describing the expanding universe do. There are numerous visualisations available which plug the numbers in for you so that you can get a feel for the evolution.
There are graphs such as fig. 1 here:
https://arxiv.org/pdf/astro-ph/0310808.pdf
(the top one has the 'common sense' units)
The same type of graphs, animated:
http://lcdm.yukterez.net/i.html#plot
A numerical calculator with graphing feature:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7-2017-02-08/LightCone_Ho7.html
(the various values are described in an easy-to understand way)

 

[electronneutrino]

In an infinitely sized universe, the singularity occurred everywhere and not at a single point in space. As to the initial rate of expansion, I can't answer. It was certainly many many times greater than it is in the present, but I don't know how rapid it might have been.

I just want to clarify my understanding of this statement about the big bang. If the universe is infinite and the big bang occurred everywhere, then the big bang constituted a universe with infinite mass energy in an infinite volume such that the mass density was finite and homogeneous as the current universe is assumed to be. As an analogy this would be like turning a screen on to get a uniform white every where all at once. Then the universe began rapid expansion and known particles came into existence along with gravity as the density decreased and thus the temperature dropped. If this is correct then I don't understand how anything larger than elementary particles could have formed. At the least there would have to be some lack of homogeneous nature through out the universe at the time or by Gauss's law there would be no unifying net force. But a lack of homogenous nature then would certainly lead to a lack now. Is this interpretation consistent with what you are saying?

 

[phinds]

I just want to clarify my understanding of this statement about the big bang. If the universe is infinite and the big bang occurred everywhere, then the big bang constituted a universe with infinite mass energy in an infinite volume such that the mass density was finite and homogeneous as the current universe is assumed to be. As an analogy this would be like turning a screen on to get a uniform white every where all at once. Then the universe began rapid expansion and known particles came into existence along with gravity as the density decreased and thus the temperature dropped. If this is correct then I don't understand how anything larger than elementary particles could have formed. At the least there would have to be some lack of homogeneous nature through out the universe at the time or by Gauss's law there would be no unifying net force. But a lack of homogenous nature then would certainly lead to a lack now. Is this interpretation consistent with what you are saying?

It is known, since we and galaxies and so forth exist, that there was inhomogeneity at the start, but it is not known WHY it was that way. In particular, one of the big mysteries is why there was an imbalance between matter and anti-matter.

 

[PeterDonis]

It is known, since we and galaxies and so forth exist, that there was inhomogeneity at the start, but it is not known WHY it was that way. In particular, one of the big mysteries is why there was an imbalance between matter and anti-matter.

This is mixing up inhomogeneity with composition. The inhomogeneity at the start (more precisely, at the end of inflation, when reheating and the big bang occurred) was in the energy density; it wasn't exactly the same everywhere. The current favored explanation of that is quantum fluctuations in the inflaton field during inflation, which would have caused fluctuations in the energy density at reheating.

The imbalance between matter and antimatter has nothing to do with the inhomogeneity in energy density; it's a separate issue for which we don't currently have a good explanation.

 

[electronneutrino]

In an infinitely sized universe, the singularity occurred everywhere and not at a single point in space. As to the initial rate of expansion, I can't answer. It was certainly many many times greater than it is in the present, but I don't know how rapid it might have been.
Those units do not change over time.
Yes, gravity has acted to slow the expansion from the very beginning as far as we know. One of the main reasons that expansion is accelerating is that gravity drops off as objects recede from each other and the density of the universe decreases over time.
I'm sorry but I'm having difficulty understanding this question.

It is known, since we and galaxies and so forth exist, that there was inhomogeneity at the start, but it is not known WHY it was that way. In particular, one of the big mysteries is why there was an imbalance between matter and anti-matter.

Then why do we assume the current universe is homogeneous. I would expect inhomogeneous properties to be exacerbated not reduced

 

[phinds]

Then why do we assume the current universe is homogeneous. I would expect inhomogeneous properties to be exacerbated not reduced

We do NOT assume any such thing, except on very large scales. Obviously if you take something the size of a galactic cluster or smaller it is not at all homogeneous. On cosmological scales, it is homogeneous.

 

[rootone]

If you were at the furthest known point in the Universe looking back at our galaxy and attempting to measure the expansion rate wouldn't time indicate the expansion rate was actually slowing down.

No, looking from there, the Milky way would be one of billions of distant galaxies, all of which are accelerating away from you.