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

[rhertz]

1. Estimated age of the Universe: 13.82 billion years (PLANCK satellite).

 

2. Hubble's constant: H = 71.06 Km.s^-1.MParsec^-1. with 1 MegaParsec = 3261600 ligth-years.

 

3. Radius of Hubble's Universe: R= c/H = 13.77 billion light-years (after which, galaxies recession > c)

 

4. Radius of observable Universe: 46.508 billion light-years (co-moving distance due to inflation)

 

5. Age = k. Hubble's radius;   k = 1.00363108 year/ligth-year.

 

6. Galaxies within observable radius > 2.10⁺¹² galaxies.

 

7. Average distance between galaxies: 17.2 million light-years.

Edited June 19, 2019 by rhertz

[Bradpitt4]

The interior of the eh is between 28-29 billion ly acrossed https://en.m.wikipedia.org/wiki/Great_Attractor

[exchemist]

How about: "Ballocks!"?  

[exchemist]

The CBR is a background noise from every piece of matter and energy in the universe. 

 

Are you are arguing for a static universe with no expansion of space. How do you explain red and BLUE shifted galaxies. 

 

Are you thinking the CBR is from random particle creation and annihilation in space happening as a continuous process, not unlike Hoyle was suggesting? before his joke caught on, and became standard model :)

 

 

 

Unlike you to make a mistake thats correctly spelt Bollocks :)

It is deliberate. Like Kingsley Amis, I prefer the older spelling, which is closer to its original meaning as a diminutive of balls. :)

[exchemist]

I've found this link from an astronomy site (I lost the original source), which has the same concept of a initial planckian universe at 3000°K.

 

https://slideplayer.com/slide/4681143/

 

If you use the Stefan-Boltzmann law, widely used in astrophysics, you have:

 

J = a. T⁴ (in watts/m2)

 

or  P/A = a. T⁴ (in watts/m2), with P: radiated power.

 

Playing a little bit with this, and assuming that the shape of the initial and final CBR can be assimilated to that

of an spherical shell of thickness =1, then the radiating surface is 4.Pi.R², and you could write:

 

P_i = 4.Pi.R_i².a.T_i⁴    ,13.5 billion years ago, and

 

P_f = 4.Pi.R_f².a.T_f⁴    , now.

 

 

Assuming that the CBR energy, at the beggining and now, is composed of energy leftovers that weren't

involved into any process of recombination or any other process involving matter (except black body energy emission

and absorption in the near infrared range), then this energy leftover is bouncing back and forth across the universe

since ever.

 

In such a case, dividing both equations side by side gives:

 

1 = R_i².R_f^-2.T_i⁴ .T_f^-4  or

 

or

 

R_f . R_i^-1 = T_i² .T_f^-2 = 10⁶  , using 3000°K and 3°K

 

what gives an expansion of 10⁶ of the initial radius of the "black body spherical shell".

 

R_i  = 15,000 light-years  (300,000 years after the BB)

 

Also, using another widely used expression in astrophysics (Wien's displacement law)

 

L_max.T = b,

 

we could say that:

 

L_maxI. L_maxf^-1 = T_i^-1T_f = 10^-3

 

or

 

L_maxI  =  10^-3 . L_maxf = 1 micrometer (being L_maxf = 1 mm, today).

 

This displacement toward the microwave range from the near infrared is due to the expansion of the universe.

 

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

 

Well, I'm done with this "crancky thing".

 

Please, proceed to mock at it (or me) at will. No ofense taken, as I was having fun with things which I don't believe.

But, the equations and conjectures are out there, coming from "academic sources", so............

That's excellent! 

 

So, whether you believe the model or not - and we are all entitled to have our reservations -  we do seem now to have at least a common understanding of what the model proposes. 

[exchemist]

There are two correction to be made, mainly because I didn't know how to write SIGMA (the Stefan-Boltzmann's Constant),

and I used "a" instead.

 

The correct Stefan-Boltzmann's formula is

 

j = SIGMA . T⁴ = P/A  (in Watts/m²)

 

and there is a real a constant (used in astrophysics), which is called radiation constant (or volume energy density), which is:

 

                                                                a = 4/c . SIGMA    (in Joules.m^-3.K^-4)

 

which allows to write the volumetric density of energy irradiated by a black body as:

 

u = a . T⁴ = E/V  (in Joules/m³)

 

Using density of energy per unit volume requires to use the volume of a sphere, instead of its surface. So, by this, final formula

changes to:

 

1 = R_i³.R_f^-3.T_i⁴ .T_f^-4  or

 

now, the total energy of the BBR radiation remains constant along the time, which gives

 

R_f³ . R_i^-3 = T_i⁴ .T_f^-4 = 10¹²  , using 3000°K and 3°K for T_i and T_f.

 

or

 

R_i = R_f . 10^-4 = 15.10⁹.10^-4 ly = 1.5 million ly  (radius of the reducted Hubble's Sphere, almost 770,000 years after the BB, and T = 3,000 °K).

 

 

 

Sorry for the mistake. I wasn't aware of the existance of a = 4/c.SIGMA.

 

With this new formula, the total energy of the initial CBR is preserved along time.

 

The change in the peak wavelength remains the same, as the ratio of temperature change still is 1/1000.

 

Question: How is that COBE, WMAP and PLANCK measured a peak wavelength of 1mm, which correspond to NOW,

when the initial peak wavelength (at 3000 °K) was 1 micrometer 13 billion years ago.

 

 

Isn't that focusing at the edge of the Hubble's Sphere (13.77 billion ly) we are looking almost equal amount of years into the past?

 

Why 1 micrometers wasn't measured, after all?

Because the metric has expanded. The effect is that the energy remains the same (no absorption by matter) whereas the volume of space it occupies is a lot greater, so its effective "temperature" is lower.

 

It is the same effect as the cosmological red shift due to metric expansion. I think. But I'm not a cosmologist.  

Edited May 13, 2019 by exchemist

[OceanBreeze]

There are two things to consider; one is the volume of the spherical universe changes according to the cube of the radius so that the number of photons per unit volume is diluted by R^-3 , and at the same time the photons are redshifted by an additional factor of R^-1 as the wavelength gets longer. So, the energy density of the CMB changes according to R^-4.

 

Incidentally, rhertz’s numbers using the light speed radius of the present universe, rather than the radius of the observable universe of 46 billion lyrs is the reason why his numbers are wrong, but at least he is making an attempt.

 

The size of the universe at last scattering was 41.8 Mlyr, not the 1.5 Mlyr that he calculated. It makes no sense to me, to use the radius of the universe as 13.77 billion lyr to calculate energy density, when we know it is much larger than that, at 46 billion lyrs!

 

(But I'm also not a cosmologist) 

 

Well, at least when I crunch the numbers they show the total energy of the CMB is conserved from the time of last scattering until today.

 

[OceanBreeze]

OceanBreeze, it's not that I'm fixated to the idea of using 13.7 Gly (visible universe) instead of 46.5 Gly (observable universe).

 

I don't understand WHY scientists persist using the radius of the Hubble's Sphere (limit where recession equals the speed of light), but

it is the way THEY DO (It's not my invention).

 

As with many other data available to check it, I use this link from the NASA's WMAP mission (which followed COBE's):

 

https://wmap.gsfc.nasa.gov/universe/bb_concepts.html

 

You can study the WMAP Universe at this link but, exploring it, it has very good and detailed info about intruments, how

the mission was done, etc.

 

I copy and paste an excerpt from the link I wrote above:

 

*********************************************************************************************************

Foundations of Big Bang Cosmology

................................

 

.

Before we discuss which of these three pictures describe our universe (if any) we must make a few disclaimers:

• 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 years. This is our so-called horizon. The Big Bang Model does not attempt to describe that region of space significantly beyond our horizon - space-time could well be quite different out there.
• It is possible that the universe has a more complicated global topology than that which is portrayed here, while still having the same local curvature. For example it could have the shape of a torus (doughnut). There may be some ways to test this idea, but most of the following discussion is unaffected.

 

 

*********************************************************************************************************

This is NASA Oficial site for WMAP satellite, and they are telling that the visible universe has a radius of 13.77 billion yl,

and that they can't measure beyond that limit.

 

Here is another link that you can use (is for a post-graduate course in astrophysics from the Virginia University):

 

http://people.virginia.edu/~dmw8f/astr5630/Topic16/Lecture_16.html

 

 

(7) Distances & Horizons

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

 

Before we start, let's recall two useful/sensible units of time and distance for cosmology:

 

  Hubble time:           t_H,o   =   H_o^-1   =   10.0 h^-1 Gyr   =   13.9 h₇₂^-1 Gyr     Hubble distance:   r_H,o   =   c / H_o   =   c t_H,o   =   13.9 h₇₂^-1 G lyr   =   4.26 h₇₂^-1 Gpc  

 

they are units comparable to the current age and visible size of the Universe.

..................................................

 

If you keep reading, they will treat the subject of observable universe, but you can't see or measure beyond the Hubble's radius.

 

I don't UNDERSTAND WHY cosmologists (and only THEM) keep talking about observable universe.

 

The only reason that I find is that the Hubble Sphere and the Hubble's Radius ARE NOT RELATIVISTIC.

 

And the calculations of the observable universe are based on GTR and BBT, being the last one relativistic.

This allows to define co-moving and proper distance at the observable universe, but is a problem that

they went into voluntarily. NOT MY PROBLEM.

 

"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 years. This 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.

I gave you the Wiki link with the size of the observable universe: According to calculations, the current comoving distance—proper distance, which takes into account that the universe has expanded since the light was emitted—to particles from which the cosmic microwave background radiation (CMBR) was emitted, which represent the radius of the visible universe, is about 14.0 billion parsecs(about 45.7 billion light-years), while the comoving distance to the edge of the observable universe is about 14.3 billion parsecs (about 46.6 billion light-years)^[10], about 2% larger. The radius of the observable universe is therefore estimated to be about 46.5 billion light-years^[11][12] and its diameter about 28.5 gigaparsecs (93 billion light-years, 8.8×10²³ kilometres or 5.5×10²³ miles)

 

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.

Edited May 13, 2019 by OceanBreeze

[OceanBreeze]

 

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, [math] \alpha \quad =\frac { 8{ \pi  }^{ 5 }{ k }^{ 4 } }{ 15{ c }^{ 3 }{ h }^{ 3 } }[/math]

 

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

 

Numerically [math]\alpha \quad =\quad 7.5657\quad E-16\quad J\quad { m }^{ -3 }\quad { K }^{ -4 }[/math]

 

Photon energy density = [math]\alpha { T }^{ 4 }[/math]

 

[math]{ T }_{ now }=\quad 2.728\quad K[/math]

 

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

 

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

 

[math]Volume\quad =\quad 4/3\quad \pi \quad { r }^{ 3 }[/math] = [math]3.453\quad E80\quad { m }^{ 3 }[/math]

 

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, [math]\alpha { T }^{ 4 }[/math] at that time was [math] 0.0613\quad J/{ m }^{ 3 }[/math]

 

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:

 

[math]\frac { 3.453\quad E80\quad { m }^{ 3 } }{ { 1100 }^{ 3 } } =\quad 2.594\quad E71\quad { m }^{ 3 }[/math]

 

That is of course the correct volume at last scattering, BUT when multiplied by the energy density of [math] 0.0613\quad J/{ m }^{ 3 }[/math], 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? :sorry:

 

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:

 

[math]\frac { 3.453\quad E80\quad { m }^{ 3 } }{ { 1100 }^{ 4 } } =\quad 2.358\quad E68\quad { m }^{ 3 }[/math]

 

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

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! :lol:

[OceanBreeze]

 

 

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.