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

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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 by rhertz
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They all appear to be measurements based on observations using current accepted theories :) does that make sense.

The observable universe is just that, if you keep going to the edge of the currently observable universe, you likely will see another 14 billion light years away, and then another and another ad finitum, the universe possibly has no edge, and no beginning.

The Big Bang and inflationary theory appears to be accepted by the majority of astrophysicists. But other theories do exist with reference to the beginnings of our universe, Roger Penrose has ideas ref separate Aeons between bangs. Quantum Loop Gravity is another theory attempting to explain everything. Many more exist, including theories which indicate a big bang never happened at all, and that the CBR can be explained in other ways. Remember Fred Hoyle coined the phrase Big Bang as a joke :)  The original theory has been altered to include inflation.

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- Only 1) and 2) are "measurements", with final numbers delivered by the PLANCK's mission team in 2018.

- The ratio between the ACTUAL observable universe and its age is 1.00. This means that what we "observe"

as far as possible, with current technology, is not something "far away" but something "old that way".

So, in the accepted concept of the universe by today, we don't look at things that are DISTANT to us but

at things that are OLDER than us, here on Earth.

So, if we accept for one instant that c is infinite, what Hubble's telescope and others measure (visible and

not visible wavelengths) is behind us in the timescale, not in the distance-scale.

The ratio almost 1 between age and real observable universe is 1.00, what means that we are looking to

ancient galaxies which, at the edge 1.00, represent the first galaxies created about 200 millions after the BB.

-  The observable universe radius is a crappy estimate for the co-moving galaxies that were formed in the early

universe, and where they should be with an inflating theory involved into calculations. If galaxies at this edge

were at 1 billion light-years from our location when the universe was 200 million years old, then they are now

45.6 times farther away due to the expansion of the universe.

-  The power that emanates from the CBR shell (my calculations) mean that the remnants of energy 200,000 years

after the explosion of the singularity, are radiating 7.55.1048 joules every second (today), what accumulates to

2.38.1056 joules  per year, and it happens without interruption since xxx years?

When will this exudation of energy stop?

- Also, according to the law of the conservation of energy, this residual of energy not transformed in matter has a

temperature (today) of 2.7ºK. The same amount of energy had to exists 13.5 billion years ago, when the

temperature was about 3,000ºK and the universe, by then, was also behaving as a planckian universe (a black body).

It is not that a black body behavior appeared at a given date, but it was always there, after most of energy transformed

into matter.

- The last concept is important, because it means that the temperature of the CBR is decreasing with time, until it reaches

(what?) the absolute zero?

- Also, the estimates of two trillions of galaxies within the observable radius, poses a doubt about the REAL ORIGIN of the

CBR, as each galaxy radiates at every possible wavelength.

- Then, what you have at my 10 points is contradictory information, which has no explanation with current theories.

This is my initial, and very superficial, analysis of those simple numbers.

I also claim that the CBR IS NOT what is believed to be, but a background noise from every piece

of matter and energy in a Hoyle's universe (a steady one), where matter and energy interacts in

actions of extinction and recreation.

So, the universe is steady and self-balancing, and there is not such a thing as a Big Bang or CBR.

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 :)

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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. :)

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I'm in a hurry, but I'd like that you may read this excellent paper:

Remaining Problems in Interpretation of the Cosmic Microwave Background

Hans-Jörg Fahr and Michael Sokaliwska

Argelander Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany

Received 25 June 2014; Accepted 7 April 2015

https://www.hindawi.com/journals/physri/2015/503106/

Joke/Note 1: Don't mess with the germans BBR, they are deep thinkers about their planckian universe, as they call it.

Note 2: Actually, the BBT states that the CBR is the leftover of the radiation soup that didn't transformed into real matter,

and that this leftover discarded about 250,000 after the Big Bang was originally at 3,000ºK. It's not my invention, and it is

the heart of the BBT. Because of that, the CBR is the ultimate proof that BB existed and that the Universe is expanding.

The link makes lots of assumptions, regarding what is expected to be found in the CBR, and then finds that the assumptions cant be supported.

I don't know if it is good idea to give you this link   but then you are an adult and can make your own mind up. There are a lot of alternative theories around ref the origins of the universe. The alternative cosmological group http://cosmology.info/

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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:

Pi = 4.Pi.Ri2.a.Ti4    ,13.5 billion years ago, and

Pf = 4.Pi.Rf2.a.Tf4    , 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 = Ri2.Rf-2.Ti4 .Tf-4  or

or

Rf . Ri-1 = Ti2 .Tf-2 = 106  , using 3000°K and 3°K

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

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

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

Lmax.T = b,

we could say that:

LmaxI. Lmaxf-1 = Ti-1Tf = 10-3

or

LmaxI  =  10-3 . Lmaxf = 1 micrometer (being Lmaxf = 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.

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

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 = Ri3.Rf-3.Ti4 .Tf-4  or

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

Rf3 . Ri-3 = Ti4 .Tf-4 = 1012  , using 3000°K and 3°K for Ti and Tf.

or

Ri = Rf . 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 by exchemist
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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.

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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:           tH,o   =   Ho-1   =   10.0 h-1 Gyr   =   13.9 h72-1 Gyr     Hubble distance:   rH,o   =   c / Ho   =   c tH,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 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.

Edited by OceanBreeze
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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? :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:

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

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! :lol:

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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.

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