Universe Expansion

[Strange]

It is stated that the expansion had started when the size of the Universe was 40 Mly and its temp was 3000K.

 

Where is this stated? It sounds wrong. Can you provide a source? What time do you think expansion started?

 

This page shows that expansion was occurring from the the initial inflationary period onward.

https://en.wikipedia.org/wiki/Chronology_of_the_universe

 

 

 

 

Eventually, there will be no open space between the clusters and all the clusters will be next to each other.

 

I assume (the statement is too vague to be sure) that at this time there would not have been any such clusters. Maybe not even stars or galaxies. What sort of timescale are you talking about?

 

We know that the expansion can only works on the open space between the clusters.

 

This is not true. The early universe was much more homogeneous than it is now. Therefore expansion would have occurred everywhere. It is only when the large scale structures formed, that some parts become more gravitationally bound.

 

 

 

So, how can we explain this contradiction?

 

Perhaps because you don't know as much as you think you do.

Edited February 3, 2016 by Strange

[swansont]

So, how can we explain this contradiction?

 

In proof-by-contradiction, it means that one or more of the assumptions was wrong. That seems the most likely explanation.

 

Therefore, as we go back on time, the clusters should be closer to each other.

 

Also the clusters will not look the same, because their composition and other characteristics change with time. You appear to be assuming that they are static, which is a horrible assumption.

[Mordred]

David all those stars, galaxies and large scale clusters account for a measly 4.6% of the energy/mass density.

 

The major portion is dark matter and dark energy.

 

A mere 4.6% is treated as mere dust at these scales.

 

http://map.gsfc.nasa.gov/universe/uni_matter.html

Edited February 4, 2016 by Mordred

[Mordred]

The average energy/mass density compared to the critical density formula determines our overall geometry.

 

[latex]\rho_{crit} = \frac{3c^2H^2}{8\pi G}[/latex]

 

[latex]\Omega=\frac{\Omega_{total}}{\Omega_{crit}}[/latex]

 

[latex]\Omega{total}=\Omega_{\Lambda}+\Omega_{dark matter}+\Omega_{baryonic matter}+\Omega_{radiation}[/latex]

 

From the chart on the link one can see baryonic matter is a minor contribution. Even less so considering matter has negligible energy/density to pressure influence.

The rate of expansion incorperates the equations of state for each particle contribution.

 

https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology)

 

These factors determine the rates of expansion. With the acceleration equation.

The acceleration equation is given as

[latex]\frac{\ddot{a}}{a}=-\frac{4\pi G\rho}{3c^2}(\rho c^2+3p)[/latex]

This leads to

[latex]H^2=\frac{\dot{a}}{a}=\frac{8\pi G\rho}{3c^2}-\frac{kc^2p}{R_c^2a^2}[/latex]

Edited February 4, 2016 by Mordred

[David Levy]

Thanks

 

This page shows that expansion was occurring from the the initial inflationary period onward.

https://en.wikipedia.org/wiki/Chronology_of_the_universe

 

That is an excellent overview from the first moment of the BB.

 

Where is this stated? It sounds wrong. Can you provide a source? What time do you think expansion started?

I assume (the statement is too vague to be sure) that at this time there would not have been any such clusters. Maybe not even stars or galaxies. What sort of timescale are you talking about?

This is not true. The early universe was much more homogeneous than it is now. Therefore expansion would have occurred everywhere. It is only when the large scale structures formed, that some parts become more gravitationally bound.

 

 

Well, I had the impression that the main phase of the expansion is fully correlated with the CMB redshift. Based on the redshift value of 1100, this expansion phase had started when the Universe temperature was - 3000K, its age was – about 400 Million years and its size was 40 Mly.

Don't you agree with that?

 

http://www.phy.duke....~kolena/cmb.htm

 

"Therefore, the drop in the CMB temperature by a factor of 1100 (= 3000 K/2.73 K) indicates an expansion of the universe by a factor of 1100 from the moment of decoupling until now".

 

In any case, clusters aren't subject to the expansion:

Because clusters aren't subject to the expansion.

 

So, if the total size of the clusters (side by side) is much bigger than the 40 Mly, than how the expansion could start at that point (40 Mly)?

Unless, you claim that all the clusters in the universe has a total size of only 40 MLY. But this might be incorrect, as our cluster by itself has a diameter of 10 Mly.

 

[Mordred]

 

 

In any case, clusters aren't subject to the expansion:

 

So, if the total size of the clusters (side by side) is much bigger than the 40 Mly, than how the expansion could start at that point (40 Mly)?

Unless, you claim that all the clusters in the universe has a total size of only 40 MLY. But this might be incorrect, as our cluster by itself has a diameter of 10 Mly.

 

 

David Clusters grow in size from the time of decoupling till now.... at the time of the CMB they were initially forming. You can't base the size of a cluster now as the size of the cluster then. The cluster size themselves grow as more and more particles decouple from thermal equilibrium. Not to mention galaxy sizes themselves have varied since then via galaxy mergers. Also the percentages of metals has been steadily growing via star fusion processes. 13 Billion years of merging etc has caused a significant change in cluster size and composition.

 

You seem to have this tendancy to jump to incorrect conclusions, I'm really not sure why this is, when you obviously have a desire to learn. Perhaps if you spend a little less time looking for faults in models you should learn why those models state what they do.

 

the anistropies in the CMB were the earliest detectable point we can measure in cluster formation. There is a large database of articles on large scale cluster formation. Particlularly on arxiv.

Edited February 6, 2016 by Mordred

[David Levy]

David Clusters grow in size from the time of decoupling till now.... at the time of the CMB they were initially forming.

 

Thanks

Sorry, but please let me know if I understand you correctly.

 

1. Is it correct that the expansion had started when the size of the universe was about 40 Mly?

2. If so, can we consider it as one cluster? (Let's call it Early Cluster)

3. What came first?

3.1. Is it the process of early cluster growing in size? (So the expansion in space can only start after this early cluster had grown

to a critical size)

3.2. Is it a process of dividing this Early Clusters into billions seeds of clusters? (So the expansion affects the open space between

those seeds, while the clusters seeds also grow in time).

Edited February 6, 2016 by David Levy

[Mordred]

Ok lets start first off at no time in the universe's history has it not been expanding.

 

If you look at the CMB maps the hot regions are overdensity regions. Those region later on become galaxy clusters. However those regions also drift. So it will not be an exact position from one location to another from CMB to today.

 

 

"However, the slight temperature variations of order a few parts in 100,000 are of enormous importance, for they essentially were early "seeds" from which all subsequent complex structures in the universe ultimately developed."

 

 

https://en.m.wikipedia.org/wiki/Structure_formation.

 

If you can follow arxiv quality articles I recommend.

 

"Formation of large scale structure of the Universe"

http://arxiv.org/abs/1209.0371

 

Here is a YouTube based on one of the best simulations this simulation took all our known laws of physics and CMB data.

 

https://m.youtube.com/watch?v=74IsySs3RGU

[Strange]

 

Thanks

Sorry, but please let me know if I understand you correctly.

 

1. Is it correct that the expansion had started when the size of the universe was about 40 Mly?

 

Of course. It was the was the expansion that caused the universe to cool enough that light could escape and cause the CMB,

 

2. If so, can we consider it as one cluster? (Let's call it Early Cluster)

There were no clusters because there were no stars at that time. Stars didn't form for another 300 million years.

http://patrickgrant.com/BBTL.htm

 

3. What came first?

3.1. Is it the process of early cluster growing in size? (So the expansion in space can only start after this early cluster had grown

to a critical size)

3.2. Is it a process of dividing this Early Clusters into billions seeds of clusters? (So the expansion affects the open space between

those seeds, while the clusters seeds also grow in time).

Neither. As the hot plasma expanded and cooled small variations in density caused some areas to start to collapse into slightly denser clouds. These eventually formed stars, galaxies, clusters and the large scale structures we see now.

http://cosmicweb.uchicago.edu/group.html

http://cosmicweb.uchicago.edu/filaments.html

[Mordred]

It's one of the most complicated and complex simulations ever done requiring several super computers.

 

Lol cross posted with Strange on edit.

 

I'll dig up the original simulation publication. Which also details that this simulation was able to accurately produce every galaxy type.

Found the original links

 

http://www.cfa.harva...du/news/2014-10

 

http://www.illustris-project.org/

Edited February 6, 2016 by Mordred

[David Levy]

Neither. As the hot plasma expanded and cooled small variations in density caused some areas to start to collapse into slightly denser clouds. These eventually formed stars, galaxies, clusters and the large scale structures we see now.

 

Sorry again that I ask too difficult questions, but I see two different types of expansions.

The first one is as you have described:

When the universe size was 40 Mly, it was "as the hot plasma expanded and cooled small variations in density caused some areas to start to collapse into slightly denser clouds".

 

But this kind of expansion might not be correlated with the second expansion which is based on the CMB redshift.

It is stated clearly that this expansion (the second one) only works on the empty space between the clusters.

Therefore, technically, the "real" expansion (which is based on the CMB redshift) can't even start its operation while the Universe is hot as plasma. (However, it doesn't contradict the idea that there was some sort of expansion).

 

Don't you think that real expansion can only start after the formation of stars, galaxies and especially clusters (Just after 300 Million years).

There were no clusters because there were no stars at that time. Stars didn't form for another 300 million years.

http://patrickgrant.com/BBTL.htm

In other words, how can we claim that the expansion (which is based on CMB redshift) had started while the Universe was plasma, while we also claim that it only works on the empty space between the clusters? (and those clusters had been formed just after another 300 Million years)

Edited February 6, 2016 by David Levy

[Strange]

But this kind of expansion might not be correlated with the second expansion which is based on the CMB redshift.

 

No. It is all the same expansion.

 

 

It is stated clearly that this expansion (the second one) only works on the empty space between the clusters.

 

It is the same expansion. But where material is held together by local gravitational forces, that will prevent them moving apart. That is what gravity does.

 

Where the gravitational force is not enough to stop things moving apart, then they will move apart.

 

I think you have the wrong model in your head; it isn't that the space between clusters causes expansion, it is that the concentrations of mass in galaxies prevent it.

 

 

Don't you think that real expansion can only start after the formation of stars, galaxies and especially clusters (Just after 300 Million years).

 

Obviously not.

 

 

In other words, how can we claim that the expansion (which is based on CMB redshift) had started while the Universe was plasma, while we also claim that it only works on the empty space between the clusters?

 

Because the uniform plasma and the uniform space between clusters are equivalent: they are homogeneous, in other words no local concentrations of mass. The same is true of the universe as a whole on very large scales. So the universe as a whole undergoes expansion, but the bits held together by gravity don't.

 

 

But the real problem is that all these descriptions are just informal analogies. You either have to look at the underlying models and understand them, or just accept that these analogies describe something interesting. You can't really understand the theory, or attempt to show it is wrong, based on these analogies. You can't extrapolate from these analogies to more complex cases or different scenarios.

 

This might help: http://arxiv.org/abs/0707.0380

 

Read the paper several times, very carefully. After you have read it at least three times, come back with questions about anything you don't understand.

 

And if you want an easy, informal, introduction to the mathematics behind it, this is a good place to start:

http://math.ucr.edu/home/baez/einstein/

[Mordred]

Redshift is a means to measure the expansion history. It is a side effect of expansion not a cause of expansion.

 

Strange covered the rest.

 

I really don't think these formulas will help much. I truly wish your math skills were higher.

 

I did this up in another thread though originally in that thread made a few errors typing from a phone etc.

 

Expansion is due to how particles interact. That interaction correlates to the ideal gas laws and thermodynamic processes.

 

Gravity causes contraction not expansion. Expansion occurs when the particle contributors to pressure overcome their self gravity.

 

It is a balancing act, near large bodies of mass, gravity exceeds the pressure causing expansion.

 

The energy/mass density to pressure relations are covered by their equations of state. I recall posting that info to you before.

 

Those equations I posted above (acceleration equation.) Plots the rate of expansion.

 

the two key values is energy/density and pressure.

 

how one can calculate an equation of state is covered in this example

You didn't catch the full correction on the first equation. Completely replace dv=pdf with DU=pdv. It's understandable your confused there. (For some dumb reason I typed f again Grr).{dumb spell check on phone}

 

[latex]DU=pdV[/latex].

 

 

Here it should read as follows with the corrections. I will add a few details.

 

First take the first law of thermodynamics.

 

[latex]dU=dW=dQ[/latex]

 

U is internal energy W =work.

 

As we dont need heat transfer Q we write this as [latex]DW=Fdr=pdV[/latex]

 

Which leads to [latex]dU=-pdV.[/latex]. Which is the first law of thermodynamics for an ideal gas.

 

[latex]U=\rho V[/latex]

[latex]\dot{U}=\dot{\rho}V+{\rho}\dot{V}=-p\dot{V}[/latex]

[latex]V\propto r^3[/latex]

[latex]\frac{\dot{V}}{V}=3\frac{\dot{r}}{r}[/latex]

 

Which leads to

 

[latex]\dot{\rho}=-3(\rho+p)\frac{\dot{r}}{r}[/latex]

 

We will use the last formula for both radiation and matter.

 

Assuming density of matter

 

[latex]\rho=\frac{M}{\frac{4}{3}\pi r^3}[/latex]

[latex]\rho=\frac{dp}{dr}\dot{r}=-3\rho \frac{\dot{r}}{r}[/latex]

 

Using the above equation the pressure due to matter gives an Eos of Pressure=0. Which makes sense as matter doesn't exert a lot of kinetic energy/momentum.

 

For radiation we will need some further formulas. Visualize a wavelength as a vibration on a string.

 

[latex]L=\frac{N\lambda}{2}[/latex]

 

As we're dealing with relativistic particles

 

[latex]c=f\lambda=f\frac{2L}{N}[/latex]

 

substitute [latex]f=\frac{n}{2L}c[/latex] into Plancks formula

 

[latex]U=\hbar w=hf[/latex]

 

[latex]U=\frac{Nhc}{2}\frac{1}{L}\propto V^{-\frac{1}{3}}[/latex]

 

Using

 

[latex]dU=-pdV[/latex]

 

using

[latex]p=-\frac{dU}{dV}=\frac{1}{3}\frac{U}{V}[/latex]

 

As well as

[latex]\rho=\frac{U}{V}[/latex]

 

leads to

 

[latex]p=1/3\rho[/latex] for ultra relativistic radiation.

 

Those are examples of how the first law of thermodynamics fit within the equations of state. There is more intensive formulas involved. In particular the Bose-Einstein statistics and Fermi-Dirac statistics but the above serves as a good approximation.

 

 

That should make more sense now again I apologize for the errors above and thanks again on the assistance in correcting. (You will note I added some missing details to assist)

 

A further+1 for the last post. It was well thought out and polite. Thanks

Note the zero pressure due to matter....

 

Prior to the CMB we have the radiation dominant era.

 

From the CMB to roughly universe age of 7.3 billion years we have the matter dominant era. During this time gravity was slowing the rate of expansion but not stopping expansion.

 

Then the cosmological took over due to the volume.

 

Now we are in the Lambda dominant era.

 

ALL OF WHICH IS DUE to energy/density to pressure influences.

 

I posted this example covering inflation and the radiation dominant era.

Sorcerer I think you need to look closely at what you mean by space expanding faster than light. The aspect your missing is that the above applies only over a huge seperation distance. Locally space expands at a mere 70 km/s/Mpc. It's only when you

a separation distance above the Hubble Horizon does the rate appear to expand faster than light. That is an incredible distance. Particle pairs cannot hope to transverse that distance without encountering normal matter and annihilating.There was a type of radiation due to expansion you may be interested in. It's rather difficult to find the cosmological application papers on it. It's disappeared from mainstream physics in terms of cosmology. However it was one presented due to inflation/expansion.

Parker radiation.

Lets run an example Considering inflation's rapid expansion rate it will provide some details on how it may have worked. (Assuming the chaotic inflation model.)inflation involves Particle/antiparticle pairs to maintain conservation of energy rules in particle production. I'll place inflation close to the GUT epock. The inflaton forms in particle pairs

[latex]w=\frac{\rho}{p}[/latex]

Let's use this relationship and describe the early universe prior to inflation then onto inflation.

A radiation dominant universe will expand as the gravitational potential is insufficient to cause a collapse.

The acceleration equation is given as

[latex]\frac{\ddot{a}}{a}=-\frac{4\pi G\rho}{3c^2}(\rho c^2+3p)[/latex]

This leads to

[latex]H^2=\frac{\dot{a}}{a}=\frac{8\pi G\rho}{3c^2}-\frac{kc^2p}{R_c^2a^2}[/latex]

where k is the curvature constant. Which during the GUT epock can be largely ignored. Via the equation of state

[latex]p=w\rho c^2[/latex]

[latex]\frac{\dot{a}}{a}=-\frac{1}{2}H^2(1+3w)[/latex]

for radiation w=-1/3 matter w=0

From this we can see a radiation dominant universe will expand. In fact it will accelerate when

[latex]w<-1/3(p<-\rho^2/3)[/latex]

When the volume sufficiently increases thereby reducing the temperature quarks, gluons and potentially the Higgs boson can drop out of thermal equilibrium. This process may potentially result in inflation as a phase change. The strong force undergoes symmetry breaking.

The simplest version of inflation is via the inflaton which then dominates expansion.

The inflaton is given by [latex]\varphi[/latex], with potential [latex]V\varphi[/latex]

The pressure of the field is

[latex]p(\varphi)=\frac{1/2\dot{\varphi}^2}{\hbar c+V\varphi}[/latex]

total energy by

[latex]E(\varphi)=\frac{1/2\dot{\varphi}}{\hbar c+V\varphi}[/latex]

with equation of state.

[latex]\frac{1/2\dot{\varphi}^2/\hbar c-V\varphi}{1/2\dot{\varphi}/\hbar c+V\varphi}[/latex]

Even inflation itself includes vacuum hence Allen Guths original inflation model is called "False Vacuum". The false vacuum is a higher energy density region that tunnels through a potential barrier to a lower vacuum region "true vacuum"

This equation describes how the universe expands ,it's more commonly called the deceleration equation. As opposed to acceleration equation.

[latex]\frac{\ddot{a}}{a}=-\frac{4\pi G\rho}{3c^2}(\rho c^2+3p)[/latex]

note the energy density to pressure terms? That derives from the FLRW metric

Just as an added perspective here is the Einstein field equation stress momentum tensor in the Minkowskii form.

[latex]T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p\eta^{\mu\nu}[/latex]

Even GR uses pressure.

I hope these examples help.

Edited February 6, 2016 by Mordred

[David Levy]

Thank you both

 

The expansion by itself is quite clear to me.

However, I still have difficulties to understand the starting point of the expansion.

It is stated:

 

It is the same expansion. But where material is held together by local gravitational forces, that will prevent them moving apart. That is what gravity does.

Where the gravitational force is not enough to stop things moving apart, then they will move apart.

 

So, with regards to the starting point -

At the moment that the size of the universe was only 40 MLY, and it includes the whole mass of the Universe - including Dark matter and dark energy, and it was a hot plasma.

Did we try to make any sort of calculation to verify the gravity force of this early Universe?

 

Gravity causes contraction not expansion. Expansion occurs when the particle contributors to pressure overcome their self gravity.

 

This is the key issue.

Gravity causes contraction not expansion.

So, what was the real gravity at that early universe?

How can we know for sure that the expansion overcome on the gravity of that early universe?

 

I have tried to set a brief calculation of the expected total mass/energy of the early universe as follow:

- The current number of galaxies in the Universe - about 500 Billion.

- Number of stars outside the galaxies - at least the same number as the whole stars in the galaxies.

Therefore, the total mass in the Universe is equivalent to about 1,000 billion galaxies.

However, there are also free atoms in the open space.

That might be correlated to the following question: What is the chance for an early atom to be placed in a star?

In other words - what is the efficiency of the early star forming process?

If it is only 50% than at least 50% of the atoms in the universe are located in the open space.

Therefore, the requested mass of that early Universe should be equivalent to 2,000 billion galaxies.

However, this actually represent only 4.6% of the whole mass/dark matter/ dark energy of the universe.

So, the early universe includes a mass/dark matter/ dark energy which is equivalent to over than 40,000 billion galaxies

Hence, what was the real gravity when whole of this mass/dark matter/ dark energy was concentrated at the size of only 40 Mly?

How could it be that the expansion had the power to overcome on that incredible gravity?

 

You can't really understand the theory, or attempt to show it is wrong, based on these analogies. You can't extrapolate from these analogies to more complex cases or different scenarios.

 

Sorry if my analogies isn't fully correct.

[Strange]

So, with regards to the starting point -

At the moment that the size of the universe was only 40 MLY, and it includes the whole mass of the Universe - including Dark matter and dark energy, and it was a hot plasma.

Did we try to make any sort of calculation to verify the gravity force of this early Universe?

 

What do you mean by "gravity force"? Gravity then would have been exactly the same as now.

 

 

How could it be that the expansion had the power to overcome on that incredible gravity?

 

Gravity is only relevant where you have concentrations of matter. When matter is homogeneously distributed then it becomes irrelevant and expansion occurs. This may seem counter-intuitive but if so, the only answer is to understand the maths.

 

But, roughly, if everything is pulling on everything else with the same force, then there is no net force on anything. The universe was filled with a homogeneous gas and so there was no net force on any part of it.

 

 

Sorry if my analogies isn't fully correct.

 

It is not your analogies. It is the analogies like "expanding space" and "clusters are held together by gravity" and "red shift caused by speed at which galaxies are receding". And basically everything other than the FLRW or Lamda-CDM model itself.

 

You are being misled by trying to extrapolate from the pop-science stories. All they can do is try to crudely explain roughly what is happening. They are not "the theory". If you want to really understand (or challenge) the big bang model, then you need to understand the theory (i.e. the mathematics).

Edited February 6, 2016 by Strange

[Mordred]

To add details to Strange answer you can calculate where expansion will overcome gravity.

 

Step one calculate the strength of the cosmological constant.

 

For this you use the critical density formula.

 

[latex] \rho_c=\frac{3H^2}{8\pi G}[/latex]

 

 

If you calculate this out it will work out to roughly to [latex] 6.0 *10^{-10} joules/metre^3[/latex]

 

or alternatively [latex]10^{-26} kg/m^3[/latex]

 

Then you calculate the strength of gravity at a given radius from a mass.

 

[latex]F=\frac{GM_1m_2}{r^2}[/latex]

 

Convert newtons to joules.

 

When the critical density becomes greater than the force of gravity. Expansion takes over.

 

 

Now as far as the average mass density (gravity vs pressure) the calculation is done when you obtain the curvature constant. k. You then compare that value to the critical density.

 

Critical density is the calculated value where the Universe stops expanding and starts contracting. (Prior to the discovery of the cosmological constant)

 

Unfortunately calculating the curvature constant is a lengthy process..

 

However you can understand the relations via this article.

 

http://cosmology101.wikidot.com/universe-geometry

 

Page 2

 

http://cosmology101.wikidot.com/geometry-flrw-metric/

 

In calculating the actual curvature constant you must consider every particle species and it's corresponding contribution to pressure as well as it's own self gravity.

 

The FLRW metric has immensely simplified this for us by providing formulas where the numerous steps are already calculated.

 

Mainly the acceleration equation

 

Here is some details on critical density.

 

"In earlier models, which did not include a cosmological constant term, critical density was initially defined as the watershed point between an expanding and a contracting Universe."

https://en.m.wikipedia.org/wiki/Friedmann_equations

Edited February 6, 2016 by Mordred

[swansont]

Don't you think that real expansion can only start after the formation of stars, galaxies and especially clusters (Just after 300 Million years).[/size]

No. If the universe wasn't expanding, it never would have cooled to the point where recombination occurred, which allowed for the CMB (which wasn't microwave back then, of course)

[David Levy]

When the critical density becomes greater than the force of gravity. Expansion takes over.

Now as far as the average mass density (gravity vs pressure) the calculation is done when you obtain the curvature constant. k. You then compare that value to the critical density.

Critical density is the calculated value where the Universe stops expanding and starts contracting. (Prior to the discovery of the cosmological constant)

Unfortunately calculating the curvature constant is a lengthy process..

 

Thanks Mordred

I do appreciate you answer.

 

Let me focus on just one issue which you have mentioned - Density

It's not clear to me how the science calculate the real density of the early Universe.

Based on my brief verification, the real mass in the universe is equivalent to at least 2,000 billion galaxies.

Never the less, if we add the effect of the dark mass and dark energy it is equivalent to 40,000 billion galaxies.

By dividing that mass to the size of the early universe, we can easily extract the density of the early universe.

However, I'm not sure that the science have used this simple calculation.

 

With regards to the dark mass/dark energy - This is the most interesting issue.

In the following article:

https://en.wikipedia.org/wiki/Chronology_of_the_universe

They ignore complitly the effect of the dark mass and dark energy in the early Universe.

How could it be that the dark mass/dark energy which covers more than 95% of the total universe mass is almost totally neglected?

 

However, it is stated that:

"If the energy density of dark energy were negative or the universe were closed, then it would be possible that the expansion of the universe would reverse and the universe would contract towards a hot, dense state. This is a required element of oscillatory universe scenarios, such as the cyclic model, although a Big Crunch does not necessarily imply an oscillatory universe. Current observations suggest that this model of the universe is unlikely to be correct, and the expansion will continue or even accelerate."

 

But, why this dark energy density is not part of the calculation for the early Universe? What about the dark mass density?

So, let me ask the following questions:

1. Do you agree that the real mass of the universe could be equivalent to about 2,000 billion galaxies? (Actually, it should be much more than that – based on the efficiency of the star forming process. As a star forming process in the early universe is based on random activity, It seems to me that it is almost as winning the lottery. 1 to 100, 1 to 1000, 1 to one million or more. In this case to form just one star, a total atoms of 100 or even one million stars might be needed…)

That could increase dramatically the density of the early Universe. Never the less, for this discussion, let's assume that it is only 50% efficiency.

2. Do you agree that the total mass/dark mass/dark energy could be equivalent to about 40,000 billion galaxies?

 

3. Did we try to calculate the real density of the early universe based on that total mass/dark enery/dark mass?

Edited February 7, 2016 by David Levy

[Strange]

It's not clear to me how the science calculate the real density of the early Universe.

 

By extrapolating back from the current density.

 

 

Based on my brief verification, the real mass in the universe is equivalent to at least 2,000 billion galaxies.

 

I'm not sure how you calculate this but (1) I assume you mean the observable universe and (2) my understanding is that the mass in galaxies is a small proportion of the mass of the universe (most of it is interstellar/intergalactic gas).

 

With regards to the dark mass/dark energy - This is the most interesting issue.

In the following article:

https://en.wikipedia.org/wiki/Chronology_of_the_universe

They ignore complitly the effect of the dark mass and dark energy in the early Universe.

I'm not sure what you base that on. It says that at 70,000 years matter starts to dominate the mass-energy of the universe (before that it was dominated by photons) and "at this stage, cold dark matter dominates".

But it also says: "However, because present theories as to the nature of dark matter are inconclusive, there is as yet no consensus as to its origin at earlier times, as currently exist for baryonic matter." So it is not known how early dark matter originated.

How could it be that the dark mass/dark energy which covers more than 95% of the total universe mass is almost totally neglected?

 

Note that dark energy would have been a far smaller proportion then, than it is now.

 

But, why this dark energy density is not part of the calculation for the early Universe? What about the dark mass density?

Why do you think it is not part of the calculation? The presence of dark matter is important in models of the early universe as well as the simulations of galaxy/large structure formation linked earlier. For example: https://en.wikipedia.org/wiki/Dark_matter#Cosmic_microwave_background

[Mordred]

Using galaxies to average the mass of the universe won't give you a good estimate.

 

The procedures are too lengthy to post but require numerous formulas.

 

Those formulas include the Fermi-Dirac and Bose Einstein statistics.

 

If you want a handy database of values don't rely on wiki.

 

Try this.

 

 

http://arxiv.org/pdf/astro-ph/0406095v2.pdf"The Cosmic energy inventory"

 

coincidentally there is a thread where someone is trying to improve mass of the universe calculations.

 

In the proper manner I might add.

 

http://www.scienceforums.net/topic/86694-observable-universe-mass/page-1

 

As you can see the calcs are rather extensive. However the cosmic inventory is backed up by experimental evidence. A rough correlation is the mass of of the universe works out to roughly equivalent to 10^90 protons.

 

One aspect you keep missing is the % of every type of particle changes due to temperature.

 

For example prior to recombination there are no atoms. The temperature is too hot for atoms to be stable.

 

This is the covered by studying big bang nucleosynthesis. The BB model did an excellent job predicting the observed % of elements in the CMB prior to actual measurement.

 

The procedures are covered in chapter 3 and 4 here

 

http://www.wiese.itp.unibe.ch/lectures/universe.pdf:" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis

 

This article has the same formulas and mannerisms as Scott Dodelson "Modern Cosmology 2nd edition"

 

In all honesty I recommend looking through the materials on my website. It's designed to provide training aids in accordance to textbooks and teachings in Cosmology courses.

 

Link is on my signature. One enjoyable article covering Freidmann is.

 

http://arxiv.org/abs/1302.1498 " The Waters I am Entering No One yet Has Crossed: Alexander Friedman and the Origins of Modern Cosmology" written by Ari Belenkiy

 

It's well informative and will provide a decent explanation of the FLRW metric.

Edited February 7, 2016 by Mordred

[David Levy]

To add details to Strange answer you can calculate where expansion will overcome gravity.

Step one calculate the strength of the cosmological constant.

For this you use the critical density formula.

 

 

If you calculate this out it will work out to roughly to

or alternatively

Then you calculate the strength of gravity at a given radius from a mass.

Convert newtons to joules.

When the critical density becomes greater than the force of gravity. Expansion takes over.

 

O.K.

 

Let's set a brief calculation based on a valid information from "The physics of the Universe".

One million light year = 9.4605284 × 10²¹ meters = about 10²²

The Diameter of Eraly Universe was 40 Million light years. That means – a radius of 20 Miliion Light years.

So the volume of this radius is:

 

R³ * / 3.14 = (20 * 10²²) ³ / 3.14 = 8/3.14 * 10⁶⁹ m^{3 =} 2.54 * 10⁶⁹ m³

 

The estimated total mass-energy of the observable Universe is:

 

http://www.physicsoftheuniverse.com/numbers.html

 

3 × 10^{52 -} Estimated mass (in kilograms) of the observable universe.

 

4 × 10^{69 -} Estimated total mass-energy (in Joules) of the observable universe.

 

So, if we set the calculation based on Joules –

 

The density of early Universe when its temp was 3000K, is:

 

4 × 10⁶⁹ / 2.54 * 10⁶⁹ m³ = 1.57 Joules/ m³

 

This value is significantly higher than the critical density of 6 * 10^-10 Joules/ m³

Therefore, it is clear that the Early universe can't expand!!!

 

Do you agree?

Edited February 8, 2016 by David Levy

[Mordred]

No this doesn't determine if the universe expands or not. To determine that you must now use the acceleration equation. You also need to determine the appropriate equation of state.

 

The set of equations you posted is used to determine when expansion takes over in terms of distance from a large scale structure or galaxy. TODAY. The 6.0*10-10 joules/m3 is the critical density of the universe TODAY not at the time of the CMB.

 

One of the terms used in the critical density formula is Hubbles Constant.

 

The value of Hubbles constant is only constant everywhere in the universe at a specific time. It's value can change with time but that change is uniform throughout the universe at that moment in time.

 

If you want to calculate if the universe expands during CMB.

 

You will need to recalculate the critical density and actual density of the universe at the specific time your calculating for.

 

Don't mix values for the universe today with values for the universe then

 

Think of it this way "what is density". It's the mass per unit volume. If you decrease the volume you increase the density. So naturally the average density will be higher in the past. However so is the critical density.

 

To be fair though I should have specified that the 6.0*10-10 joules/m^3 is the critical density today.

Edited February 9, 2016 by Mordred

[Mordred]

Now just as a test question.

 

You now know a volume change results in a change in density. What other factor will result in a density change (assuming the same number moles of particles) ?

 

 

Here is some details to help with Hubbles constant.

 

https://en.m.wikipedia.org/wiki/Hubble%27s_law

 

"The value of the Hubble parameter changes over time, either increasing or decreasing depending on the value of the so-called deceleration parameter q, "

 

Took me a bit to remember this formula to calculate the Hubble constant at a specific time using today's values.

 

[latex]H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}[/latex]

 

If you run this formula you will find per Mpc the rate of expansion is significantly higher than today. If you graph it you will see an inverted slope.

 

Using Planck values at

 

Z=1100 H=23257.149 H/H_O age 000368 Gy meaning H then compared to H today

 

Z=774.038 H=13248.939 age 000659 Gy

Z=484.919 H=6345.461 age 001410 Gy

Z=303.652 H=3075.757 age 002966 Gy

Z=190.095 H=1503.414 age 006162 Gy

Z=105.56 H=619.028 age 001516 Gy

Z=65.809 H=305.560 age 030908 Gy

Z=28.513 H=89.233 age 0.106812 Gy

Z=17.508 H=44.233 age 0.216042 Gy

Z=5.472 H=9.170 age 1.047912 Gy

Z=3.058 H=4.608 age 2.105181 Gy

Z=1.014 H=1.790 age 5.805752 Gy

Z=0(now) H=1.0 age 13.7872206 Gy

 

 

should give you the curve if not use the Cosmo calc on my signature set number of steps to 100, S_upper to 1100 open column definitions select Age H/H_O and redshift. Press graph or chart then hit calculate.

 

(Key note this is the compared rate of expansion then and now PER Mpc.)

 

Not the rate of expansion from Earth to the Cosmological event horizon (observable universe). Which is accelerating. Reason being the increase rate of number of Mpc between Earth and the Cosmological event horizon.

Edited February 9, 2016 by Mordred

[David Levy]

No this doesn't determine if the universe expands or not. To determine that you must now use the acceleration equation. You also need to determine the appropriate equation of state.

 

The set of equations you posted is used to determine when expansion takes over in terms of distance from a large scale structure or galaxy. TODAY. The 6.0*10-10 joules/m3 is the critical density of the universe TODAY not at the time of the CMB.

 

One of the terms used in the critical density formula is Hubbles Constant.

 

The value of Hubbles constant is only constant everywhere in the universe at a specific time. It's value can change with time but that change is uniform throughout the universe at that moment in time.

 

If you want to calculate if the universe expands during CMB.

 

You will need to recalculate the critical density and actual density of the universe at the specific time your calculating for.

 

Don't mix values for the universe today with values for the universe then

 

Think of it this way "what is density". It's the mass per unit volume. If you decrease the volume you increase the density. So naturally the average density will be higher in the past. However so is the critical density.

 

To be fair though I should have specified that the 6.0*10-10 joules/m^3 is the critical density today.

 

Thanks

 

That is fully clear.

We must use the correct value of Hubbles constant

 

Here is some details to help with Hubbles constant.

 

https://en.m.wikipedia.org/wiki/Hubble%27s_law

 

"The value of the Hubble parameter changes over time, either increasing or decreasing depending on the value of the so-called deceleration parameter q, "

 

If you run this formula you will find per Mpc the rate of expansion is significantly higher than today. If you graph it you will see an inverted slope.

 

Using Planck values at

 

Z=1100 H=23257.149 H/H_O age 000368 Gy meaning H then compared to H today

 

Z=774.038 H=13248.939 age 000659 Gy

Z=484.919 H=6345.461 age 001410 Gy

Z=303.652 H=3075.757 age 002966 Gy

Z=190.095 H=1503.414 age 006162 Gy

Z=105.56 H=619.028 age 001516 Gy

Z=65.809 H=305.560 age 030908 Gy

Z=28.513 H=89.233 age 0.106812 Gy

Z=17.508 H=44.233 age 0.216042 Gy

Z=5.472 H=9.170 age 1.047912 Gy

Z=3.058 H=4.608 age 2.105181 Gy

Z=1.014 H=1.790 age 5.805752 Gy

Z=0(now) H=1.0 age 13.7872206 Gy

 

should give you the curve if not use the Cosmo calc on my signature set number of steps to 100, S_upper to 1100 open column definitions select Age H/H_O and redshift. Press graph or chart then hit calculate.

 

So, lets use the maximal value of H:

Z=1100 H=23257.149 H/H_O age 000368 Gy meaning H then compared to H today

H= 23257. = 2.3 10⁴

 

Based on the following formula for critical density:

 

 

The current (today) value of H is 1.

Z=0(now) H=1.0 age 13.7872206 Gy

So, the impact of the new maximal H is:

 

H² = (2.3 10⁴⁾² = 5.3 * 10⁸

 

Therefore, the updated maximal critical density is:

 

6 * 10^-10 * H² Joules/ m³ = 6 * 10^-10 * 5.3 * 10⁸ = 3.18 * 10^-1 Joules/ m³

 

So, that value represents the maximal critical density.

However, based on my calculation:

 

The density of early Universe when its temp was 3000K, is:

4 × 10⁶⁹ / 2.54 * 10⁶⁹ m³ = 1.57 Joules/ m³

Therefore, even now the density of early Universe is higher than the critical maximal density.

 

Please also be aware that I have only used the total Mass/energy of the visible universe, So the real density of the whole Universe should be even higher than 1.57 Joules/ m³.

 

Hence, it is clear that even under the maximal conditions, the expansion can't take over.

 

Do you agree?

Edited February 10, 2016 by David Levy

[imatfaal]

I haven't followed this thread but it is clear that you maths is awry

[latex]

 

\rho_c=\frac{3.H^2}{8.\pi.G}

[/latex]

 

As given by you (and not by Mordred) the top of the division is larger than one. G is much much smaller than one - but is on the bottom so its effect is to increase size of answer; there is no way it is going to be as small as you suggest. Just look at the powers of ten

 

[latex]

\rho_c \approx \frac{10^1.10^4.10^4}{10^1.10^1.10^{-11}} \approx \frac{10^9}{10^{-9}} \approx 10^{18}

[/latex]

 

 

You really need to understand these equations before you go plugging numbers in to make a point - but even before that you need to have a feeling from the maths of whereabouts your answers must lie.

 

Once you have the maths right you can first - before plugging in numbers and contradicting people - make sure that you understand whether you are using the correct physical constant, it is in the correct form, and that it is in the right units - ie please don't just rerun the equation and say here is an even more unlikely answer; find out why you are getting odd answers first*

 

 

*Take a look at the title row of Mordred's table