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The Observed Universe, Our Universe, Our Big Bang.



 
 
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  #1  
Old July 4th 14, 07:24 PM posted to sci.astro.research
Nicolaas Vroom
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Posts: 216
Default The Observed Universe, Our Universe, Our Big Bang.

If you want to understand physics (astronomy) you have to use terminilogy
independent of any human point of view.
IMO Max Tegmark does not follow this idea when he defines Our Universe
in his book "The Mathematical Universe" as: (page 120)
The part of the physical reality we can in principle observe.
Phillip Helbig in his document:
http://www.astro.multivax.de:8000/he..._universe.html
writes: Tegmark uses "our universe" to denote that which is more commonly
described as the "observable universe"
Tegmark also writes at page 121:
"Our Universe contains about 10^11 galaxies etc. This is certainly a
lot of stuff, but could there exist even more, farther away in space?
As we saw, inflation predicts that there is"

Alan Guth in his book "The Inflationary Universe" writes at page 186:
"We find that the entire universe is expected to be at least 10^23
times larger than the observed universe"
Alan Guth also uses the term "presently observed universe" which is
even more "difficult".

IMO when you study science from human perspectif you make a mistake.
The problem is that the "observable universe" from some one
living at the Andromeda Galaxy or 1 billion ly away at present
is different from ours. Part is overlapping, while we all have
a common origin: the Big Bang.
IMO it only makes sense to talk about "Our Universe" meaning all
that is "created" by the Big Bang and that is described
by Friedmann's equation (and not use the term observable universe)
The R(t) in that equation should express the size of "Our Universe"
during its evolution and not what is observed.

The simulations of the friedmann equation as described in
http://users.telenet.be/nicvroom/fri...20equation.htm
show that the distance of the events at the observed lightray is
small relative to the radius of the Universe at these events.
(except for the earliest events)

When we call "Our Universe" homogeneous it should be related
based on the above definition.
The same when we discuss inflation.

What the simulation also shows that the initial distance (v0 * dt)
of the Universe with the first iteration has almost no influence
on the final distance at present.

To define parallel Universes within "Our Universe" as defined
above, IMO is not realistic.

That does not mean that there could not be more Big Bangs.
I do not want to exclude that. A such you can define the
concept of Our Big Bang implying that there are more,
which happened at different moments.
The implications are speculations.

Nicolaas Vroom
  #2  
Old July 5th 14, 07:23 PM posted to sci.astro.research
Phillip Helbig---undress to reply
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Posts: 629
Default The Observed Universe, Our Universe, Our Big Bang.

In article , Nicolaas Vroom
writes:

If you want to understand physics (astronomy) you have to use terminilogy
independent of any human point of view.


The important thing is to use it consistently.

IMO Max Tegmark does not follow this idea when he defines Our Universe
in his book "The Mathematical Universe" as: (page 120)
The part of the physical reality we can in principle observe.


This is what most people refer to as "the observable universe" or "the
part of the universe within the particle horizon".

Phillip Helbig in his document:
http://www.astro.multivax.de:8000/he..._universe.html
writes: Tegmark uses "our universe" to denote that which is more commonly
described as the "observable universe"
Tegmark also writes at page 121:
"Our Universe contains about 10^11 galaxies etc. This is certainly a
lot of stuff, but could there exist even more, farther away in space?
As we saw, inflation predicts that there is"


Right. Tegmark does use the term differently than most people, but he
does define his terms and use them consistently.

Alan Guth in his book "The Inflationary Universe" writes at page 186:
"We find that the entire universe is expected to be at least 10^23
times larger than the observed universe"


Right. He uses it in the more traditional way. This would be Tegmark's
Level I multiverse (and his "observed universe" is Tegmark's "universe").

Alan Guth also uses the term "presently observed universe" which is
even more "difficult".


Not really, as the observed universe grows with time. This is trivial,
really: The observed universe is that part of the universe from which
light could have reached us (ignoring absorption, scattering etc). By
symmetry, it is the sphere defined by photons which left our position in
space at the big bang. It always increases in size in co-moving
coordinates.

IMO when you study science from human perspectif you make a mistake.
The problem is that the "observable universe" from some one
living at the Andromeda Galaxy or 1 billion ly away at present
is different from ours. Part is overlapping, while we all have
a common origin: the Big Bang.


A rose, by any other name, would smell as sweet. It doesn't matter what
you call it, as long as you use the terms consistently. Personally, I
would use a different terminology than Tegmark here, but as long as he
defines his terms and uses them consistently, that's OK. It's just a
question what is useful. One could do much worse. For example, one
could call the observable universe "George", or "
FEWfiwejfoiewofweoifjwoijwioejfwoieu38479878342$%$ %$@" and Tegmark's
Level II multiverse "Ingrid" or "843980$#@*$#(oewfhuwhEFEWOW". For
that matter, one could call the number 17 "that which survives" and the
number 478357838573075397520 "my departed consciousness". Would this be
useful? No. Could one do consistent mathematics with it? Yes, but it
would be more difficult than necessary.

IMO it only makes sense to talk about "Our Universe" meaning all
that is "created" by the Big Bang and that is described
by Friedmann's equation (and not use the term observable universe)
The R(t) in that equation should express the size of "Our Universe"
during its evolution and not what is observed.


This is the traditional meaning, and the way I usually use the term. Of
course, it DOES make sense to talk about the observable universe if we
are interested in what we can, in principle, observe.

To define parallel Universes within "Our Universe" as defined
above, IMO is not realistic.


It's just a question of terminology:

traditional Tegmark
------------------- -------------------
observable universe universe
universe Level I multiverse
other universes Level II multiverse

That does not mean that there could not be more Big Bangs.
I do not want to exclude that. A such you can define the
concept of Our Big Bang implying that there are more,
which happened at different moments.


Right. But then you need a name for them, "other universes" for
example.

Other people take an opposite approach to Tegmark and DEFINE universe to
be "all that exists" (which Tegmark calls "external physical reality"),
i.e. at least Tegmark's Level II multiverse.

Note that, in general, none of the terms above corresponds to the Hubble
sphere.
  #3  
Old July 7th 14, 07:56 AM posted to sci.astro.research
Jos Bergervoet
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Posts: 126
Default The Observed Universe, Our Universe, Our Big Bang.

On 7/5/2014 8:23 PM, Phillip Helbig---undress to reply wrote:
In , Nicolaas Vroom

...
Tegmark also writes at page 121:
"Our Universe contains about 10^11 galaxies etc. This is certainly a
lot of stuff, but could there exist even more, farther away in space?
As we saw, inflation predicts that there is"


Right. Tegmark does use the term differently than most people, but he
does define his terms and use them consistently.


Wchich nevertheless makes things unnecessary confusing.
Tegmark damages his own cause by reverting to this kind
of word game. (Unless his cause is just to create a
spectacular picture to make it into the news headlines.)

For
that matter, one could call the number 17 "that which survives"


Things like that are routinely done:
integer, parameter :: that_which_survives = 17
or
INT that which survives = 17

... Would this be useful?
No.


I think one can find different opinions as well!

.....
That does not mean that there could not be more Big Bangs.
I do not want to exclude that. A such you can define the
concept of Our Big Bang implying that there are more,
which happened at different moments.


Right. But then you need a name for them, "other universes" for
example.


Yes if you define a *new* concept. But you do not
need to deliberately use novel names for existing
concepts (suggestive names that sound interesting,
as Tegmark does with his "level I multiverse").

Other people take an opposite approach to Tegmark and DEFINE universe to
be "all that exists" (which Tegmark calls "external physical reality"),


I wonder if the same happened with "world" after
people realized that there are other planets..
Especially after Newton's unified theory of forces
either on earth or far away from it, there might
have been a sense that everything now belongs to our
"world." (And the opposite view, that world should
just apply to our own planet, apparently won.)

--
Jos
  #4  
Old July 8th 14, 09:14 AM posted to sci.astro.research
Phillip Helbig---undress to reply
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Posts: 629
Default The Observed Universe, Our Universe, Our Big Bang.

In article , Jos Bergervoet
writes:

Tegmark also writes at page 121:
"Our Universe contains about 10^11 galaxies etc. This is certainly a
lot of stuff, but could there exist even more, farther away in space?
As we saw, inflation predicts that there is"


Right. Tegmark does use the term differently than most people, but he
does define his terms and use them consistently.


Wchich nevertheless makes things unnecessary confusing.
Tegmark damages his own cause by reverting to this kind
of word game. (Unless his cause is just to create a
spectacular picture to make it into the news headlines.)


I think his reason for this is to have his Level I multiverse be
something which is essentially mainstream; that might make the other
multiverses easier to swallow. From his point of view, everything which
is not in principle observable now but nevertheless exists is in some
level of multiverse. Thus, it has its own inner logic.

Note that some people have used "universe" to mean "all that exists",
by definition, so even without Tegmark the terminology is not uniform.

Yes if you define a *new* concept. But you do not
need to deliberately use novel names for existing
concepts (suggestive names that sound interesting,
as Tegmark does with his "level I multiverse").


If that were it then, yes, it would be as silly as calling it Joe.
However, in a book about the various levels of multiverse, it does have
its own logic.

I wonder if the same happened with "world" after
people realized that there are other planets..
Especially after Newton's unified theory of forces
either on earth or far away from it, there might
have been a sense that everything now belongs to our
"world." (And the opposite view, that world should
just apply to our own planet, apparently won.)


To some extent, yes. "Plurality of worlds" was once taken to mean not
just other planets, but other systems including fixed stars, planets, a
central star etc.
  #5  
Old July 10th 14, 08:48 AM posted to sci.astro.research
Nicolaas Vroom
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Posts: 216
Default The Observed Universe, Our Universe, Our Big Bang.

Op zaterdag 5 juli 2014 20:23:15 UTC+2 schreef Phillip Helbig
In article , Nicolaas Vroom
writes:

IMO Max Tegmark does not follow this idea when he defines Our Universe
in his book "The Mathematical Universe" as: (page 120)
The part of the physical reality we can in principle observe.


This is what most people refer to as "the observable universe" or "the
part of the universe within the particle horizon".


The question is if this definition is independent of humans. IMO it is not.
IMO the radius R (R=1) of the friedmann equation is independent of humans.
It should describe all that is changed (created) as the result of the
Big Bang.
When you study Supernovae 1A the distance is a function of "humans" i.e.
it is a function of the position from were the distance is measured.

Tegmark also writes at page 121:
"Our Universe contains about 10^11 galaxies etc. This is certainly a
lot of stuff, but could there exist even more, farther away in space?
As we saw, inflation predicts that there is"


Right. Tegmark does use the term differently than most people, but he
does define his terms and use them consistently.

I'am not saying he does not.

Alan Guth also uses the term "presently observed universe" which is
even more "difficult".


Not really, as the observed universe grows with time. This is trivial,
really: The observed universe is that part of the universe from which
light could have reached us (ignoring absorption, scattering etc).


When you study the distance from which light can reach you it is not that
simple.
Locally at present this distance is zero. When you go backwards in time the
distance increases lineair with time in the past. However the further
away you go backwards in time the increase diminishes because space expansion
has to be taken into account. When you go back more (roughly 7 b years after
the BB) the distance is constant. More earlier the distance from which light
can reach you decreases. At the time of the Big Bang the distance is again zero.

When you consider the maximum distance (as defined above), then this distances
increases lineair as a function of the time after the Big Bang.
However the space occupied is much smaller as Our Universe.
Inflation has "nothing" to do with this.

By symmetry, it is the sphere defined by photons which left our
position in space at the big bang. It always increases in size
in co-moving coordinates.

We have to be carefull. Our Universe increases in size as described
by the friedmann equation.
How ever that is not what we observe.
At present of our universe we can only observe a small part.
Out side that space we can not observe galaxies in their present state.
However those same galaxies we can presently observe when they
were younger and the distance towards us was smaller.

IMO it only makes sense to talk about "Our Universe" meaning all
that is "created" by the Big Bang and that is described
by Friedmann's equation (and not use the term observable universe)
The R(t) in that equation should express the size of "Our Universe"
during its evolution and not what is observed.


This is the traditional meaning, and the way I usually use the term. Of
course, it DOES make sense to talk about the observable universe if we
are interested in what we can, in principle, observe.


IMO that makes only sense when we study supernovae 1A. See above.
Of course when we study the evolution of "Our Universe" it should
not be in conflict with what is observed.

That does not mean that there could not be more Big Bangs.
I do not want to exclude that. A such you can define the
concept of Our Big Bang implying that there are more,
which happened at different moments.


Right. But then you need a name for them, "other universes" for
example.


No problem. Our Universe and Our Big Bang.
Other universes and other Big Bangs.
  #6  
Old July 11th 14, 09:49 AM posted to sci.astro.research
Phillip Helbig---undress to reply
external usenet poster
 
Posts: 629
Default The Observed Universe, Our Universe, Our Big Bang.

In article , Nicolaas Vroom
writes:

This is what most people refer to as "the observable universe" or "the
part of the universe within the particle horizon".


The question is if this definition is independent of humans. IMO it is not.
IMO the radius R (R=1) of the friedmann equation is independent of humans.
It should describe all that is changed (created) as the result of the
Big Bang.
When you study Supernovae 1A the distance is a function of "humans" i.e.
it is a function of the position from were the distance is measured.


Right. The observable universe obviously depends on our position: we
are at the centre of it. It is like the horizon on Earth: the average
person can see about 11 km if there are no obstructions.

When you study the distance from which light can reach you it is not that
simple.
Locally at present this distance is zero. When you go backwards in time the
distance increases lineair with time in the past. However the further
away you go backwards in time the increase diminishes because space expansion
has to be taken into account. When you go back more (roughly 7 b years after
the BB) the distance is constant. More earlier the distance from which light
can reach you decreases. At the time of the Big Bang the distance is
again zero.


What you are referring to is the proper distance at the time the light
was emitted. In the context of the obervable universe, we are
interested in the proper distance NOW of the most distanct objects which
we can see.

When you consider the maximum distance (as defined above), then this
distances
increases lineair as a function of the time after the Big Bang.
However the space occupied is much smaller as Our Universe.
Inflation has "nothing" to do with this.


True. What Tegmark means is that if the universe is almost flat as a
result of inflation, then the universe (his Level I multiverse) is much
larger than our observable universe (his universe). This is true
without inflation as well, of course. However, a nearly flat universe
is a robust prediction of inflation (non-flat inflationary models are
contrived), so his statement is true: from inflation follows that the
universe is much bigger than the observable universe. It doesn't
REQUIRE inflation, though.

Your description of the distance at time of light emission holds for all
geometries. If the universe is positively curved with a radius of
curvature just a few times the Hubble length, then there is more to the
universe than we can see, but not THAT much more.

By symmetry, it is the sphere defined by photons which left our
position in space at the big bang. It always increases in size
in co-moving coordinates.

We have to be carefull. Our Universe increases in size as described
by the friedmann equation.
How ever that is not what we observe.
At present of our universe we can only observe a small part.
Out side that space we can not observe galaxies in their present state.
However those same galaxies we can presently observe when they
were younger and the distance towards us was smaller.


Still, the radius of the observable universe always increases in
comoving coordinates. The observable universe is, by definition, that
part of the universe which we can in principle observe.

IMO that makes only sense when we study supernovae 1A. See above.
Of course when we study the evolution of "Our Universe" it should
not be in conflict with what is observed.


There are more things in the universe than just supernovae Ia. :-)
  #7  
Old July 11th 14, 09:51 AM posted to sci.astro.research
Nicolaas Vroom
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Posts: 216
Default The Observed Universe, Our Universe, Our Big Bang.

Op dinsdag 8 juli 2014 10:14:08 UTC+2 schreef Phillip Helbig:

Tegmark also writes at page 121:
"Our Universe contains about 10^11 galaxies etc.
As we saw, inflation predicts that there is ... even more "


I think his reason for this is to have his Level I multiverse be
something which is essentially mainstream; that might make the other
multiverses easier to swallow. From his point of view, everything which
is not in principle observable now but nevertheless exists is in some
level of multiverse. Thus, it has its own inner logic.


At page 120 Max Tegmark writes:
Our Universe: The spherical region of space from which light has had time
to reach us during the 14 billion years since our Big Bang - basically
this:
Beside that there is sphere from the image of the front page of his book:
See: http://space.mit.edu/home/tegmark/mathematical.html

The problem is that the radius of this sphere at the time of the creation
of the CMB 300000 years after the BB was a very small.
7 b years after the BB the radius was roughly 5 b lightyears.
At present the radius is again very small. We can only observe a tiny
bit of Our universe (All what is created after the BB) at present.

Mak Tegmark also calls this our observable Universe.
IMO that name is correct and is mainly used to study Supernovae data
and to calculate the cosmological parameters.
To call this Our Universe is wrong because IMO that name should refer
to all what is created after the Big Bang and is described by the
Friedmann equation which Radius roughly speaking increases lineair with time

As such our observable Universe is much more a subset of Our Universe.
In Tegmark his terminology:
Our Universe is much more a subset of Level 1 multiverse.

The important part is that this is direct consequence of the Big Bang and
expanding space concept and has almost nothing to do with the inflation theory

Note that some people have used "universe" to mean "all that exists",
by definition, so even without Tegmark the terminology is not uniform.


This definition is in agreement with the idea of one BB and that all
that exists is created thereafter.
Tegmark defines the Physical Reality: Everything that exists.

Nicolaas Vroom
http://users.pandora.be/nicvroom/
  #8  
Old July 11th 14, 09:23 PM posted to sci.astro.research
Phillip Helbig---undress to reply
external usenet poster
 
Posts: 629
Default The Observed Universe, Our Universe, Our Big Bang.

In article , Nicolaas Vroom
writes:

At page 120 Max Tegmark writes:
Our Universe: The spherical region of space from which light has had time
to reach us during the 14 billion years since our Big Bang - basically
this:


Right; this is his definition (what some call the "observable
universe").

Beside that there is sphere from the image of the front page of his book:
See: http://space.mit.edu/home/tegmark/mathematical.html

The problem is that the radius of this sphere at the time of the creation
of the CMB 300000 years after the BB was a very small.


Right. However, what Tegmark is referring to is the proper distance NOW
of the most distant objects we can see, not the distance when the
radiation we detect now was emitted. (Of course, in co-moving
coordinates there is no distinction.)

7 b years after the BB the radius was roughly 5 b lightyears.
At present the radius is again very small.


It doesn't shrink in an expanding universe, neither in co-moving nor in
proper distance. What you are thinking of is that there is a maximum
distance AT THE TIME OF EMISSION. Yes, that's true. Don't confuse this
with the proper distance NOW.

We can only observe a tiny
bit of Our universe (All what is created after the BB) at present.


It depends on what you mean by "at present". We observe events on our
backward light-cone (and have other evidence for events within it). The
CURRENT radius of the observable universe is measured in dozens of
light-years (more than the 13.7 which is the age of the universe---that
is the light-travel time, but expansion increases the distance NOW,
though of course we cannot observe EVENTS, only OBJECTS, which are NOW
at that distance). If the radius of curvature of the universe is much
larger than the Hubble radius (as seems to be the case), then it is
indeed the case that the universe is much larger (perhaps infinitely
larger) than the observable universe. (Note that, in general, the
Hubble sphere does not correspond to any sort of horizon and so, in
general, is not equivalent to the observable universe. However, except
for rather special cosmological models, it is larger or smaller by at
most an order of magnitude, so is useful as a ball-park figure.)

Mak Tegmark also calls this our observable Universe.
IMO that name is correct and is mainly used to study Supernovae data
and to calculate the cosmological parameters.


I'm not sure why you are dwelling on the supernovae data here.
Obviously, all our empirical information about the universe comes from
the observable universe. This includes CMB, galaxy surveys, QSOs etc
and not just supernovae.

To call this Our Universe is wrong because IMO that name should refer
to all what is created after the Big Bang and is described by the
Friedmann equation which Radius roughly speaking increases lineair with time


Again, different authors have different terminologies. Tegmark is not
the first to use a different terminology. As long as it is consistent,
it is just a matter of taste. On a similar not, some authors have a
dimensionless scale factor, some don't. However, all agree when
discussing actually observable quantities.

As such our observable Universe is much more a subset of Our Universe.
In Tegmark his terminology:
Our Universe is much more a subset of Level 1 multiverse.


Right. I would say "observable universe" and "universe" for his
"universe" and "Level I multiverse". There is no confusion about
concepts, though---only different terminology.

The important part is that this is direct consequence of the Big Bang and
expanding space concept and has almost nothing to do with the inflation theory


Right.
  #9  
Old July 11th 14, 09:29 PM posted to sci.astro.research
Nicolaas Vroom
external usenet poster
 
Posts: 216
Default The Observed Universe, Our Universe, Our Big Bang.

Op vrijdag 11 juli 2014 10:49:20 UTC+2 schreef Phillip Helbig:

Right. The observable universe obviously depends on our position: we
are at the centre of it. It is like the horizon on Earth: the average
person can see about 11 km if there are no obstructions.


As I mentioned before what is sense of defining a physical concept
(ie Our Universe) centered around our point of view.

Locally at present this distance is zero. When you go backwards in
time the distance increases lineair with time in the past.
However the further away you go backwards in time the increase
diminishes because space expansion has to be taken into account. When
you go back more (roughly 7 b years after the BB) the distance is constant.
More earlier the distance from which light can reach you decreases.
At the time of the Big Bang the distance is again zero.


What you are referring to is the proper distance at the time the light
was emitted.

From a physical object, which light we receive now.
The most distant physical object in principle we can observe is the CMB
(or very close)

In the context of the obervable universe, we are
interested in the proper distance NOW of the most distanct objects which
we can see.


To calculate the proper distance Now of the CMB radiation you have to use the
Friedmann equation. (Now approximate 35 b light years)
The Friedmann equation describes all what created as a result of the Big Bang.
IMO the two are identical ?

When you consider the maximum distance (as defined above), then this
distances
increases lineair as a function of the time after the Big Bang.
However the space occupied is much smaller as Our Universe.
Inflation has "nothing" to do with this.


True. What Tegmark means is that if the universe is almost flat as a
result of inflation, then the universe (his Level I multiverse) is much
larger than our observable universe (his universe). This is true
without inflation as well, of course. However, a nearly flat universe
is a robust prediction of inflation (non-flat inflationary models are
contrived), so his statement is true: from inflation follows that the
universe is much bigger than the observable universe. It doesn't
REQUIRE inflation, though


Alan Guth in his book writes at page 286:
"To me the most impressive piece of evidence for inflation is the flatness
problem - the closeness of the mass density of the early universe to the
critical value."
IMO that means that Lambda and omega(Lambda) are zero.
Which is in conflict which the currently accepted value that omega(Lambda)
is 0,73 and omega(M) = 0.27 using Lambda=0,01155
With Lambda = 0,1155 Omega(Lambda) becomes 0,998
and the total size 110 b Light years at present.

IMO the most important issue to discuss is the influence of inflation
on the Friedmann equation and the total size of of Our Universe now.
This is what Alan Guth describes in his book at page 185.
When you study study figure 10.6 my interpretation is, that with inflation
the size is the same but the age is a fraction of a second younger.

The result of my simulations are the same as described he
http://users.telenet.be/nicvroom/fri...20equation.htm
The parameter to study is V0, which defines the speed (distance)
of the first iteration.

Nicolaas Vroom
  #10  
Old July 12th 14, 10:16 AM posted to sci.astro.research
Phillip Helbig---undress to reply
external usenet poster
 
Posts: 629
Default The Observed Universe, Our Universe, Our Big Bang.

In article , Nicolaas Vroom
writes:

Right. The observable universe obviously depends on our position: we
are at the centre of it. It is like the horizon on Earth: the average
person can see about 11 km if there are no obstructions.


As I mentioned before what is sense of defining a physical concept
(ie Our Universe) centered around our point of view.


It's just a word. Whether you call it the universe, the observable
universe, or George doesn't matter.

What you are referring to is the proper distance at the time the light
was emitted.

From a physical object, which light we receive now.
The most distant physical object in principle we can observe is the CMB
(or very close)

In the context of the obervable universe, we are
interested in the proper distance NOW of the most distanct objects which
we can see.


To calculate the proper distance Now of the CMB radiation you have to use the
Friedmann equation. (Now approximate 35 b light years)


Right.

The Friedmann equation describes all what created as a result of the Big Bang.
IMO the two are identical ?


Right. If you like, the Friedmann equation describes what we call the
universe and Tegmark calls the Level I multiverse.

"To me the most impressive piece of evidence for inflation is the flatness
problem - the closeness of the mass density of the early universe to the
critical value."
IMO that means that Lambda and omega(Lambda) are zero.


No; it means that the sum is 1.

Which is in conflict which the currently accepted value that omega(Lambda)
is 0,73 and omega(M) = 0.27 using Lambda=0,01155
With Lambda = 0,1155 Omega(Lambda) becomes 0,998
and the total size 110 b Light years at present.


Where did you get the idea that flatness implies that lambda and Omega
are zero?

Inflation fairly robustly predicts an almost flat universe. How likely
such a universe is without inflation is not clear. It is difficult to
talk about probability in the context of the universe.

IMO the most important issue to discuss is the influence of inflation
on the Friedmann equation and the total size of of Our Universe now.
This is what Alan Guth describes in his book at page 185.
When you study study figure 10.6 my interpretation is, that with inflation
the size is the same but the age is a fraction of a second younger.


Inflation is over very, very, very early. After that, traditional
cosmology explains what we need. The effect of inflation is to make the
sum of lambda and Omega very close to 1 or, in other words, the radius
of curvature much larger than the Hubble radius.
 




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