Size Of Observable Universe, Hubble's Constant, Age And Inflation. What Results?

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#18 rhertz

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Posted 13 May 2019 - 05:33 PM

"Because the universe has a finite age (~13.77 billion years) we can only see a finite distance out into space: ~13.77 billion light yearsThis is our so-called horizon."

The above statement is quite simply wrong! 13.77 billion years is the light travel time.

The observable universe, also known as the Hubble volume, is the region of space that it is theoretically possible for us to observe, small enough that light from the furthest regions has had sufficient time to reach Earth since the Big Bang. This region of space has a diameter of approximately 92.94 billion light-years, centered on the planet Earth. Each different portion of space has its own visible universe, some overlapping, some not.

There are countless other links saying the same thing.

As I said, when you are calculating the total energy, or the energy density, it makes no sense at all to use the radius of the light travel time, and I don't know of any cosmologists who would do that.

I tell you what; go ahead and do your calculations for energy density and total energy, using the 13.77 Blyr radius as your size, then work out the total energy of the CMB, then work that back to the time of last scattering and show what the size of the universe was then and that the total energy of the CMB is the same, conserved.

Show the numerical answers and show the energy is the same  then and now, if you can.

Maybe you can convince me you are right?

When you are done I will post my numbers for comparison.

Fair enough?

This is nothing personal, but we should both want to get to the bottom of this for a better understanding.

Of course it's not personal! I agree with you!

My problem is this:

the Hubble's Radius, at which galaxies start to recede faster than light.

They call this radius as the one for VISIBLE Universe. So, COBE, WMAP and PLANCK maps of anisotropies

are a 2D projection of a sphere with the HUBBLE RADIUS.

2) When relativity and inflation enter into the picture, it appears a OBSERVABLE RADIUS. But, at the same time,

cosmologists agree that TODAY it's impossible to get signals beyond VISIBLE RADIUS.

I believe that even them don't know what they are saying.

Another thing: Co-moving and proper distances appear when they talk about the OBSERVABLE universe.

And both distances are ALMOST IDENTICAL (they tell why, but I don't get it).

Finally, I know when to stop. I think that I'll never will be able to understand the "observable" radius, specially

in the way it's defined: It exist, but nothing can be measure at its edge with TODAY's TECHNOLOGY.

And that excuse just kill any desire I can have to understand it, because I feel that it's completely non-logical.

I have NO FORMATION in astronomy, astrophysics or cosmology. I only know things that I read since childhood

with books like Isaac Assimov's "The Universe", some Atlas books on stars, constellations and galaxies, and my

own inference using my technical basis on math and physics, plus analytical thinking.

Only recently, when I wrote a 30 pages document about the history of the Black Body Radiation (1859-1900), I

became aware of Stefan, Wien, Planck and others whose works are currently applied at astrophysics and cosmology.

Also, don't forget that I'm a non-believer on relativity (none of them, but specially GTR), black holes and the BBT plus inflation.

The fact that I'm fooling around these theories, RESPECTING THEM, is because I need to crunch some numbers to avoide being bored.

Also, I can develop my own CONCEPTS (not theories) about the Universe and the building of physics in general. I find interesting to

criticize what seems unlogical for me.

No other agenda than what I expressed above. Just a curious but renegade mind fooling around.

But one thing is certain: If something is ILL DEFINED, even when I dislike the original idea, I express myself

against it, showing the fails, paradoxes or fallacies.

And I do this just for fun, as a "food for thought".

Why don't you try to enter at NASA COBE's and WMAP's sites or at ESA's PLANCK satellite mission

and try to find out which is the radius they used for the different anisotropies maps?

I think that you'll be surprised with the answer. One thing is astrophysics (the engineering branch of

astronomy) and a very different thing is cosmology (the philosophical branch of astronomy).

I hope you may understand me (I dropped Wiki as a serious source of information almost when it started,

and because of that I seek data at academic place or gov. institutions).

Are we OK?

P.S.: I promise you that, when I find the mood, I'll try to understand co-moving and proper

distances, and inflation & GTR and its impact on the observable universe of 45.6 Gyl radius.

#19 rhertz

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Posted 13 May 2019 - 05:45 PM

I forgot to put some pics that I found at Google (Images) when I searched exactly "visible universe".

It's a pity that this forum blocks data from Quora, but it's OK.

This is from: https://earthsky.org...erse-sdss-sloan

This is from: http://hubblesite.or...oughs/cosmology

This one is from: https://www.shutters...Uz_IspcQIHA-1-0

#20 rhertz

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Posted 13 May 2019 - 06:00 PM

I forgot to put some pics that I found at Google (Images) when I searched exactly "visible universe".

It's a pity that this forum blocks data from Quora, but it's OK.

This one is from: https://www.shutters...Uz_IspcQIHA-1-0

Now I'm mad. I didn't notice that the third pic contains a THIRD RADIUS, inbetween the visible and observable.

Also, now I've learned something else.

The middle range radius is assigned to expansion effects.

The observable universe radius is DUE TO the calculations about DARK MATTER!

Are this cosmologists making romm to accomodate this "matter"?

They are crazy beyond belief, but get paychecks of six digits, if they wrote enough "papers".

Shame on these blood-suckers.

#21 OceanBreeze

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Posted 14 May 2019 - 04:31 AM

Are we OK?

we're fine. it is the rest of the world that has the problem

P.S.: I promise you that, when I find the mood, I'll try to understand co-moving and proper

distances, and inflation & GTR and its impact on the observable universe of 45.6 Gyl radius.

I'm going to hold you to that, starting now!

First, the radiation constant, $\alpha \quad =\frac { 8{ \pi }^{ 5 }{ k }^{ 4 } }{ 15{ c }^{ 3 }{ h }^{ 3 } }$

Where c is the speed of light, k is Boltzmann's constant, and h is Planck's constant.

Numerically $\alpha \quad =\quad 7.5657\quad E-16\quad J\quad { m }^{ -3 }\quad { K }^{ -4 }$

Photon energy density = $\alpha { T }^{ 4 }$

${ T }_{ now }=\quad 2.728\quad K$

So, energy density of the CMB photons is $4.19\quad E-14\quad J/{ m }^{ 3 }$

All we need now to find the total energy of the CMB photons is the volume of the observable universe.

The Radius is 46 E9 lyrs, = 4.35 E26 m

$Volume\quad =\quad 4/3\quad \pi \quad { r }^{ 3 }$ = $3.453\quad E80\quad { m }^{ 3 }$

Total energy of CMB photons = 1.45 E67 Joules

The object now is to show that this value is conserved; that it is the same now as at the time of last scattering.

To do that, I use the linear scaling factor of 1100. That is, at last scattering the universe’s linear dimensions were 1100 times smaller than today.

That scaling factor also applied to the Temperature, so that 2.728 K today corresponds to 3000 K at decoupling and last scattering.

So, $\alpha { T }^{ 4 }$ at that time was $0.0613\quad J/{ m }^{ 3 }$

Now, here is where it is easy to go wrong . . .

If you calculate the volume of the universe at last scattering by taking the cube of the scaling factor, and dividing that into the present-day volume, you get:

$\frac { 3.453\quad E80\quad { m }^{ 3 } }{ { 1100 }^{ 3 } } =\quad 2.594\quad E71\quad { m }^{ 3 }$

That is of course the correct volume at last scattering, BUT when multiplied by the energy density of $0.0613\quad J/{ m }^{ 3 }$, that will not get back to the total value of energy that must be conserved, that was calculated to be 1.45 E67 Joules.

So what gives?

Well, here is a paper that explains why, but the only part that you need to read is the first few sentences, which I quote here:

“According to present cosmological views the energy density of CMB (Cosmic Microwave Background) photons, freely propagating through the expanding cosmos, varies proportional to 1/S^4 with S being the scale factor of the universe. This behavior is expected, because General Theory of Relativity, in application to FLRW- (Friedmann-Lemaitre-RobertsonWalker) cosmological universes, leads to the conclusion that the photon wavelengths increase during their free passage through the spacetime metrics of the universe by the same factor as does the scale factor S . This appears to be a reasonable explanation for the presently observed Planckian CMB spectrum with its actual temperature of about 2.7 K, while at the time of its origin after the last scattering during the recombination phase its temperature should have been about 3000 K, at an epoch of about 380 ky after the Big Bang, when the scale of the universe S r was smaller by roughly a factor of S/S r = 1+zr = 1100 compared to the present scale S = S 0 of the universe”

(I strongly advise that you do NOT read the rest of this paper)

So, you see, while the volume varies according to the cube of the scaling factor, the energy density varies according to the fourth power!

The simplest way to apply this is to calculate an “effective volume” of the early universe:

$\frac { 3.453\quad E80\quad { m }^{ 3 } }{ { 1100 }^{ 4 } } =\quad 2.358\quad E68\quad { m }^{ 3 }$

Now, when this is multiplied by the energy density of $0.0613\quad J/{ m }^{ 3 }$,

We find that the total energy of the CMB in the early universe was 1.45 E67 Joules same as today.

I hope that clears up all of your questions while opening up even deeper doubts and confusions!

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#22 rhertz

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Posted 14 May 2019 - 08:35 AM

we're fine. it is the rest of the world that has the problem

I'm going to hold you to that, starting now!

First, the radiation constant, $\alpha \quad =\frac { 8{ \pi }^{ 5 }{ k }^{ 4 } }{ 15{ c }^{ 3 }{ h }^{ 3 } }$

Where c is the speed of light, k is Boltzmann's constant, and h is Planck's constant.

Numerically $\alpha \quad =\quad 7.5657\quad E-16\quad J\quad { m }^{ -3 }\quad { K }^{ -4 }$

Photon energy density = $\alpha { T }^{ 4 }$

${ T }_{ now }=\quad 2.728\quad K$

So, energy density of the CMB photons is $4.19\quad E-14\quad J/{ m }^{ 3 }$

All we need now to find the total energy of the CMB photons is the volume of the observable universe.

The Radius is 46 E9 lyrs, = 4.35 E26 m

$Volume\quad =\quad 4/3\quad \pi \quad { r }^{ 3 }$ = $3.453\quad E80\quad { m }^{ 3 }$

Total energy of CMB photons = 1.45 E67 Joules

The object now is to show that this value is conserved; that it is the same now as at the time of last scattering.

To do that, I use the linear scaling factor of 1100. That is, at last scattering the universe’s linear dimensions were 1100 times smaller than today.

That scaling factor also applied to the Temperature, so that 2.728 K today corresponds to 3000 K at decoupling and last scattering.

So, $\alpha { T }^{ 4 }$ at that time was $0.0613\quad J/{ m }^{ 3 }$

Now, here is where it is easy to go wrong . . .

If you calculate the volume of the universe at last scattering by taking the cube of the scaling factor, and dividing that into the present-day volume, you get:

$\frac { 3.453\quad E80\quad { m }^{ 3 } }{ { 1100 }^{ 3 } } =\quad 2.594\quad E71\quad { m }^{ 3 }$

That is of course the correct volume at last scattering, BUT when multiplied by the energy density of $0.0613\quad J/{ m }^{ 3 }$, that will not get back to the total value of energy that must be conserved, that was calculated to be 1.45 E67 Joules.

So what gives?

Well, here is a paper that explains why, but the only part that you need to read is the first few sentences, which I quote here:

“According to present cosmological views the energy density of CMB (Cosmic Microwave Background) photons, freely propagating through the expanding cosmos, varies proportional to 1/S^4 with S being the scale factor of the universe. This behavior is expected, because General Theory of Relativity, in application to FLRW- (Friedmann-Lemaitre-RobertsonWalker) cosmological universes, leads to the conclusion that the photon wavelengths increase during their free passage through the spacetime metrics of the universe by the same factor as does the scale factor S . This appears to be a reasonable explanation for the presently observed Planckian CMB spectrum with its actual temperature of about 2.7 K, while at the time of its origin after the last scattering during the recombination phase its temperature should have been about 3000 K, at an epoch of about 380 ky after the Big Bang, when the scale of the universe S r was smaller by roughly a factor of S/S r = 1+zr = 1100 compared to the present scale S = S 0 of the universe”

(I strongly advise that you do NOT read the rest of this paper)

So, you see, while the volume varies according to the cube of the scaling factor, the energy density varies according to the fourth power!

The simplest way to apply this is to calculate an “effective volume” of the early universe:

$\frac { 3.453\quad E80\quad { m }^{ 3 } }{ { 1100 }^{ 4 } } =\quad 2.358\quad E68\quad { m }^{ 3 }$

Now, when this is multiplied by the energy density of $0.0613\quad J/{ m }^{ 3 }$,

We find that the total energy of the CMB in the early universe was 1.45 E67 Joules same as today.

I hope that clears up all of your questions while opening up even deeper doubts and confusions!

I remind you what I wrote posts ago:

Only recently, when I wrote a 30 pages document about the history of the Black Body Radiation (1859-1900), I

became aware of Stefan, Wien, Planck and others whose works are currently applied at astrophysics and cosmology.

This is an excerpt where I write about the Stefan-Boltzmann's Law and its application either as the total radiant power

of a BB surface or the energy density it creates. As you can see, I'm keen aware of these formulae and its uses in astronomy,

Here is an excerpt of my blog:

---------------------------------------------------------------------------------------------------------

When you apply the derivation for energy density u = E/V, you get  E = V.u.

As V = 4/3 Pi r3, the total energy depends only on the third power of the sphere's radius (not the fourth).

Energy density depends on the fourth power of the absolute temperature.

So, as u = a.T4, then E = 4/3 Pi r3 a T4, and this is the TOTAL ENERGY within a BLACK BODY CAVITY.

Now, follow me on this: The ratio between Energy at 3000 ºK (Ei) and the Energy at 2.728 ºK (Ef) has to be equal to ONE (Conservation of CMB energy).

So, Ei/Ef = ri3.Ti4/(rf3.Tf4) = 1

then, you obtain the relationship that is valid ONLY if the fundamental constants k, h and c hasn't changed in 13 billion years!

(ri/rf)3 = (Tf/Ti)4

And, with this equation, you can play back and forth with radii and temperatures 13.5 billion years ago and now.

You can, later, derivate the current energy of the CMB (and ONLY this energy), in Joules per m3.

This equation doesn't solve the problem of radii of observable and visible universe, because the first concept

didn't have any meaning 300,000 years after the BB and after the exponential inflation happened. There is not

GTR that can be applied 13.5 billion years ago, when the universe had a TOTAL radius of about 1.5 million yl.

This is a widely graph used by cosmologists, which contains the original exponential inflation and the radius of the universe.

The scale to use is 1 yl = 9.6.1015 meters.

Don't forget that I'm not confused. I just have doubts, which is a different thing.

I'll read the paper, now that you told me not to do so (as a child).

Cheers,

Richard

P.S.: The more I research, the more I'm convinced that the paper I wrote about the history

of the BB radiation (1859-1900) contains most of the equations being used within the BBT.

So, cosmologists are using (to the least) 120 years theories (shame on them).

#23 OceanBreeze

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Posted 14 May 2019 - 11:01 AM

When you apply the derivation for energy density u = E/V, you get  E = V.u.

As V = 4/3 Pi r3, the total energy depends only on the third power of the sphere's radius (not the fourth).

Energy density depends on the fourth power of the absolute temperature.

So, as u = a.T4, then E = 4/3 Pi r3 a T4, and this is the TOTAL ENERGY within a BLACK BODY CAVITY.

No, and I explained in detail why this is wrong. The energy density of matter does indeed vary with the cubic of the scaling factor, according to the change in volume. But, the energy density of a volume of photon radiation changes according to the fourth power of the scaling factor.

The reason is the wavelength of the photon emission changes according to the same change in scale.

The paper I cited gives a nice explanation:

“According to present cosmological views the energy density of CMB (Cosmic Microwave Background) photons, freely propagating through the expanding cosmos, varies proportional to 1/S^4 with S being the scale factor of the universe. This behavior is expected, because General Theory of Relativity, in application to FLRW- (Friedmann-Lemaitre-RobertsonWalker) cosmological universes, leads to the conclusion that the photon wavelengths increase during their free passage through the spacetime metrics of the universe by the same factor as does the scale factor S . This appears to be a reasonable explanation for the presently observed Planckian CMB spectrum with its actual temperature of about 2.7 K, while at the time of its origin after the last scattering during the recombination phase its temperature should have been about 3000 K, at an epoch of about 380 ky after the Big Bang, when the scale of the universe S r was smaller by roughly a factor of S/S r = 1+zr = 1100 compared to the present scale S = S 0 of the universe”

If you don’t like that, (and I know you don't), you can do a search and find many references that support this, unlike your usual unfounded assertions that are based on nothing but your opinion. By the way, using a bold red font to make your unfounded assertions does not make them any less wrong.