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# de Sitter space acceleration horizon?

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Still trying to get my head around current cosmology theory. Here goes -

In de Sitter space, as the universe went through its accelerating expansion, any point in the universe had an horizon at which point space was expanding faster than the speed of light, preventing anti-particles recombining with real particles. I understand this is the theory of how particles came into existence.

What I don't understand - I thought relativity tells us that the speed of light is a constant, regardless of the relative speed of the observer/observed, which in my small brain would contradict the existence of the horizon.

Please can someone put me out of my misery?

thanks

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Trying to capture my lack of understanding in words has allowed me to think on this some more, and I think I've answered my own question!

That said, I'd still be interested in replies....

thanks

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Quite simple if you think of expanding universe not as things moving away from each other because of their "speed" but rather space between them expanding.

Let's say that there is fixed amount of "new" space that is created per unit length per unit time.

Now imagine two points in space - one emitting light, and one about to "receive" it. If they are far away, expanding universe means that light will never reach "receiving" point. Why? because as light goes certain distance in unit time - remaining distance is big enough that all space created between "current light position" and "receiver point" is larger than light traveled in unit time.

In another words - light travels N meters, but N+1 meter is created in remaining space (one that light is yet to travel). All points from which light will reach us "in limit" (meaning after infinite amount of time, but will still reach us) define horizon - everything beyond that will never reach us.

Do note that rate of space "creation" (scale factor) is not constant in time.

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Correct me if I’m wrong but, speed of light constant applies to Matter itself, not expansion.

Edited by Sunshine

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7 minutes ago, vlaiv said:

Quite simple if you think of expanding universe not as things moving away from each other because of their "speed" but rather space between them expanding.

Let's say that there is fixed amount of "new" space that is created per unit length per unit time.

Some things started making far more sense to me when I realised expansion could be viewed this way.

James

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1 minute ago, JamesF said:

Some things started making far more sense to me when I realised expansion could be viewed this way.

James

Yes, maybe easiest way to visualize would be expanding ball (2d space), or just a plain circle (1d space) - where radius is growing with time. In 2d surface case - balloon being inflated is excellent analogy.

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In fact we still have no theory of how particles came to out number anti particles. The net result of the particle anti particle annihilation is the CMB. CMB "photons" out number proton by about 10^8 if I remember correctly

Regards Andrew

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there is a theory that on the larger scales we may have a bit different laws of physics.... Nano<Newton<Einstein<Something Else

Edited by RolandKol

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2 hours ago, vlaiv said:

Quite simple if you think of expanding universe not as things moving away from each other because of their "speed" but rather space between them expanding.

Let's say that there is fixed amount of "new" space that is created per unit length per unit time.

Now imagine two points in space - one emitting light, and one about to "receive" it. If they are far away, expanding universe means that light will never reach "receiving" point. Why? because as light goes certain distance in unit time - remaining distance is big enough that all space created between "current light position" and "receiver point" is larger than light traveled in unit time.

In another words - light travels N meters, but N+1 meter is created in remaining space (one that light is yet to travel). All points from which light will reach us "in limit" (meaning after infinite amount of time, but will still reach us) define horizon - everything beyond that will never reach us.

Do note that rate of space "creation" (scale factor) is not constant in time.

Thanks vlaiv. Yes, that was my revelation when I thought about it some more, but you explain it very well!

So, back to my question, and relativity - I presume then that "c" is constant only when the relative velocity of observer and observed is < light speed.

Regarding your balloon analogy, I prefer the analogy of raisins in a fruit-loaf being baked in the oven. All the raisins move away from each other as the loaf expands, the raisins being the "matter" and the dough being the intervening "space". I think this is easier to visualise the 3-dimensionality of the expansion.

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1 hour ago, RolandKol said:

there is a theory that on the larger scales we may have a bit different laws of physics.... Nano<Newton<Einstein<Something Else

Isn't that more speculation than theory?  To be a theory, doesn't it have to have measurable predictions? (please don't be fooled into thinking I know what I'm talking about!)

Edited by Astrokev

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10 hours ago, Astrokev said:

Isn't that more speculation than theory?  To be a theory, doesn't it have to have measurable predictions? (please don't be fooled into thinking I know what I'm talking about!)

Yep, I probably used a bad term in this statement, it should probably be "ideas". Just simply, there are some scientist who think it is not logical to rely and support Bing Bang theory by adding Matter you do not see and you do not know what is made from and some kind of mysterious energy which is able to expand the space itself like a balloon... Just think a bit more about it, and it sounds completely "un-real"... Of-course, if we will compare it to Nano world, - not so funny at all... However, -

They claim, - From the point of logic, the current model has the "holes" filled with some Mysterious Dark stuff to make the theory work? Just like Einstein did his constant, - but in a opposite way, - isn't it?  Their ideas are based on the same observations, just instead of using "Dark / Mysterious" stuff to explain it, - they look into different ways.

I hope, they will come up with something less Mysterious and Dark!

Edited by RolandKol
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10 hours ago, Astrokev said:

So, back to my question, and relativity - I presume then that "c" is constant only when the relative velocity of observer and observed is < light speed.

Relativity just says that c is constant in sense - what ever frame of reference you measure it in, you will get the same value.

If two subjects are approaching each other with velocity v and one shines a torch at other - other will not measure speed of that light to be c+v as we would naively think. We would think that because for low speeds in classical limit things behave like that - speed addition is valid - but this is only in classical limit when involved speeds are small. If we had enough precision in our measurement we would in fact see that this is not true and classical speed addition is in fact wrong - for even small speeds (but error is so small that for all practical purposes speed addition approximation is valid).

In above sense c is constant, and further implication of that is that no object can accelerate to the speed of light or past it (measured from any reference frame).

In fact, space expansion and galaxies moving away from each other as if having certain speed relative to each other is equivalent. This presents problem with moving with speeds greater than that of speed of light, unless we observe two things: no acceleration took place, therefore "no accelerating to the speed of light or beyond it" was not violated. We also say that some galaxies move relative to each other with speeds greater than speed of light - but first "postulate" is also not violated - you can't measure that speed as such galaxies are in fact in causally disconnected regions of space - no signal can ever travel between them, so no measurement can be performed.

49 minutes ago, RolandKol said:

Yep, I probably used a bad term in this statement, it should probably be "ideas". Just simply, there are some scientist who think it is not logical to rely and support Bing Bang theory by adding Matter you do not see and you do not know what is made from and some kind of mysterious energy which is able to expand the space itself like a balloon... Just think a bit more about it, and it sounds completely "un-real"... Of-course, if we will compare it to Nano world, - not so funny at all... However, -

They claim, - From the point of logic, the current model has the "holes" filled with some Mysterious Dark stuff to make the theory work? Just like Einstein did his constant, - but in a opposite way, - isn't it?  Their ideas are based on the same observations, just instead of using "Dark / Mysterious" stuff to explain it, - they look into different ways.

I hope, they will come up with something less Mysterious and Dark! ﻿

The thing is that both dark matter and dark energy owe their "Mysterious" nature to the press rather than scientists.

Dark matter was discovered, if I'm not mistaken, not as a consequence of big bang cosmology, but rather much more mundane and "closer" causes - such as rotational speed of stars in spiral galaxies, behavior of galaxy cluster and such. We call it dark not because it's mysterious, but because it does not shine in EM spectrum and is really dark. Well, it's invisible really, not just dark, and one would not be able to "hold" it to observe it, since it does not interact with EM and can't bond into larger clumps because of this - it is in form of elementary particles.

Dark energy on the other hand is not term scientists use. I think proper term would be vacuum energy, or vacuum negative pressure. This again is not something new. From QFT it is long known that there is zero point energy of vacuum, or lowest energy value of quantum harmonic oscillator.

Problem with lambda CDM model and QFT zero point energy is large discrepancy in measured and calculated value of zero point energy. This is simply because we yet don't understand how to properly calculate zero point energy as it involves summing over all quantum fields and all modes of oscillation - which gives rise to infinite values. Then we apply some common sense limits, but we still get enormous values for energy (a lot of modes really). This is where famous discrepancy of 10^120 comes from - measured negative vacuum pressure being 10^120 smaller than calculated values.

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57 minutes ago, vlaiv said:

Dark matter was discovered, if I'm not mistaken, not as a consequence of big bang cosmology, but rather much more mundane and "closer" causes - such as rotational speed of stars in spiral galaxies, behavior of galaxy cluster and such. We call it dark not because it's mysterious, but because it does not shine in EM spectrum and is really dark. Well, it's invisible really, not just dark, and one would not be able to "hold" it to observe it, since it does not interact with EM and can't bond into larger clumps because of this - it is in form of elementary particles.

Dark energy on the other hand is not term scientists use. I think proper term would be vacuum energy, or vacuum negative pressure. This again is not something new. From QFT it is long known that there is zero point energy of vacuum, or lowest energy value of quantum harmonic oscillator.

Problem with lambda CDM model and QFT zero point energy is large discrepancy in measured and calculated value of zero point energy. This is simply because we yet don't understand how to properly calculate zero point energy as it involves summing over all quantum fields and all modes of oscillation - which gives rise to infinite values. Then we apply some common sense limits, but we still get enormous values for energy (a lot of modes really). This is where famous discrepancy of 10^120 comes from - measured negative vacuum pressure being 10^120 smaller than calculated values.

As I recall, they could not explain why further galaxies spin at the same rate as the inner ones in the galaxy cluster and why the outer ones simply do not "fly" away as they spin too fast, -  the only way to make our usual formulas work was to add Mass, in fact, to add around 25% more (and we do not speak about kilograms here  ), - and it works now, but only after you add 25% more of "something".

So it was more like mathematic solution, so our computers would be able to perform modeling.
This is exactly what Einstein did with his constant, probably thats why Vera Ruben have not received a Nobel price... as her "dark matter" was a hypothesis which fit the formulas nicely, - not the fact.

I hope, we have a new Hubble somewhere, - who will sort this puzzle out properly before we end up in graves

As per D Energy, - the difference 10^120 only shows scientist do not understand it's nature properly, the statement - our universe expands into the vacuum is a presumption at the first place, the logical guess, not the fact...

Our current main model simply does not work in all the areas....

Speed of light is constant, yes, but we know only about our "close surrounding" ,  - light travels slower int the water, our known top speed is in "vacuum" (almost vacuum), - no one has idea how it behaves "Outside" the known universe. In fact, it is not completely clear how EM waves / Light  travel at all,  and in "what stuff" it travels. What happens if someone is intelligent on/close to the limit of the universe and shines the laser outside?

My opinion on @Astrokev question, - no one yet knows or understands it... there are some better or worse predictions, - but.... we are still far away from the real solution.

Edited by RolandKol
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21 minutes ago, RolandKol said:

As I recall, they could not explain why further galaxies spin at the same rate as the inner ones in the galaxy cluster and why the outer ones simply do not "fly" away as they spin too fast, -  the only way to make our usual formulas work was to add Mass, in fact, to add around 25% more (and we do not speak about kilograms here  ), - and it works now, but only after you add 25% more of "something".

So it was more like mathematic solution, so our computers would be able to perform modeling.
This is exactly what Einstein did with his constant, probably thats why Vera Ruben have not received a Nobel price... as her "dark matter" was a hypothesis which fit the formulas nicely, - not the fact.

I hope, we have a new Hubble somewhere, - who will sort this puzzle out properly before we end up in graves

As per D Energy, - the difference 10^120 only shows scientist do not understand it's nature properly, the statement - our universe expands into the vacuum is a presumption at the first place, the logical guess, not the fact...

Our current main model simply does not work in all the areas....

Speed of light is constant, yes, but we know only about our "close surrounding" ,  - light travels slower int the water, our known top speed is in "vacuum" (almost vacuum), - no one has idea how it behaves "Outside" the known universe. In fact, it is not completely clear how EM waves / Light  travel at all,  and in "what stuff" it travels. What happens if someone is intelligent on/close to the limit of the universe and shines the laser outside?

My opinion on @Astrokev question, - no one yet knows or understands it... there are some better or worse predictions, - but.... we are still far away from the real solution.

Actually we do have quite solid understanding of what is going on. It just looks like we don't have a clue

You have to be careful with statements like - out there, there might be some new physics .... So far most of things that we have discovered actually fit extremely well with physics as we understand it. It's not about individual explanations or individual phenomena - it's about how everything comes together when we apply the same physics we understand here.

Take for example expanding universe. If you take a simple premise - universe is homogeneous and isotropic on large scales, and model with a simple physics - even Newtonian mechanics - you will end up with solution that is either expanding or contracting.

Another example would be CMB - it has black body distribution, it has cooled down, but if you "rewind" the time and let it behave like universe was indeed expanding according to above - you end up with temperature of around 3000K. If you take totally different branch of physics and observe how plasma behaves (opaque to EM) and you take density of matter in such early universe and temperature - you end up with exact same thing - 3000K is ionization temperature for given hydrogen density (it can actually be much larger like 10000K if you change density, but for given parameters of average density of matter, and we can measure that by observing how much galaxies there is on average in universe - if you rewind everything back - it just fits).

If you take the fact that there is dark matter that does not interact with EM, but only via gravity, and there is ordinary matter that scatters with EM photons and put everything together at those temperatures - and solve equations you will get certain oscillations in pressure/density - like with stars - gravity pulls together - photons push apart - until equilibrium. Add dark matter and you get more or less stable oscillations. Calculate density of things, use the speed of light as maximum possible speed, and calculate amplitude of such oscillations.

Then you look at density of galaxies in modern time and you conclude that they bunch up in filaments that correspond to amplitude of these baryon oscillations. You take your CMB graph and do Fourier analysis and you conclude that frequency/wavelength of disturbances correspond to above oscillations.

You of course take bunch of other measurements - like relation of red shift to luminosity for distant objects, and it matches model for expanding universe that you get when you solve equations for certain energy densities.

There are discrepancies and things that we don't understand - like why we obtain slightly different value of present day Hubble constant via different methods, or why is there more matter than antimatter (it has to do with various things - some of which we actually know and have verified experimentally such as CP symmetry breaking), but overall things fit together extremely well.

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35 minutes ago, vlaiv said:

Actually we do have quite solid understanding of what is going on. It just looks like we don't have a clue

You have to be careful with statements like - out there, there might be some new physics .... So far most of things that we have discovered actually fit extremely well with physics as we understand it. It's not about individual explanations or individual phenomena - it's about how everything comes together when we apply the same physics we understand here.

I do not say it does not work, otherwise we would not have SatNavs or any robots on Mars and etc

It actually works, but with lots of "N" - filled with "something"  that most likely fits.  I look at it as an opened bottle without the cap, - you block it with a paper and it works, yes it holds the watter inside even if the bottle is upside down...

There are lots of fundamental questions which are not yet answered and all predictions about what's happening with the universe at it's edges/limits, should not be taken as facts yet... As "maybe" only, or "most likely" as very optimistic option, - we cannot test and examine the edges... this the complete "Dark area" in my opinion.

Another opinion: Newton was right, it took time to raise people like Einstein and Schroedinger, who managed to discover different laws on different scales of our Universe, Hubble managed to correct Einstein a bit, now others correcting the Hubble,  - and I think, we will have more in both directions, in a very large and  in a very small scales also.

At the end, does the space expands faster than speed of light at the edges of universe? it looks like it should... but is it really? No one has proofed it yet.

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43 minutes ago, RolandKol said:

I do not say it does not work, otherwise we would not have SatNavs or any robots on Mars and etc

It actually works, but with lots of "N" - filled with "something"  that most likely fits.  I look at it as an opened bottle without the cap, - you block it with a paper and it works, yes it holds the watter inside even if the bottle is upside down...

There are lots of fundamental questions which are not yet answered and all predictions about what's happening with the universe at it's edges/limits, should not be taken as facts yet... As "maybe" only, or "most likely" as very optimistic option, - we cannot test and examine the edges... this the complete "Dark area" in my opinion.

Another opinion: Newton was right, it took time to raise people like Einstein and Schroedinger, who managed to discover different laws on different scales of our Universe, Hubble managed to correct Einstein a bit, now others correcting the Hubble,  - and I think, we will have more in both directions, in a very large and  in a very small scales also.

At the end, does the space expands faster than speed of light at the edges of universe? it looks like it should... but is it really? No one has proofed it yet.

You mention edges of universe - there is no such thing. Space expands at a certain rate, currently at about 70km/s per Mpc - meaning for each mega parsec of distance rate of expansion of universe is such that object will be moving away from us at about 70km/s (67km/s or 73km/s - depending on data used to calculate - one of problems in modern cosmology).

This is rate of expansion between us an our neighboring galaxies as well as rate of expansion between galaxies billion light years away (local rate of expansion). Space expands at that rate "all over the place" and this rate of expansion is governed by all the "stuff" in universe (meaning energy in different form - matter, light, vacuum). We can't say that space is expanding faster than light. What we can say instead is that two objects - far enough, look like they are "receding" from each other at speed greater than the speed of light. In fact this is what is causing horizon that we experience. Space is probably many times larger than our observable universe - our measurements lack precision to determine this yet. As far as we know, our universe is flat within 1% of uncertainty of measurement. This could simply mean that it's positively curved (or negatively) with very large radius. If you were to measure curvature of earth on 1km squared patch of desert with meter stick - you would have no idea that you are on spherical object - thing would look flat to you.

So we have no idea if space is indeed flat and infinite (or maybe finite in extent but without bounds - violating our assumption of isotropy), positively curved with finite radius (and again no boundary), negatively curved and infinite, ....

There is one great assumption in place when we discuss cosmology - that is cosmological principle. It's our assumption that we are in isotropic and homogeneous universe, and that we hold no special position in it - extension of Copernican principle.

If we go by above principle, then there are only three geometries that fit - flat and infinite (euclidean space), negatively curved and infinite (hyperbolic geometry) and positively curved and finite (3 sphere) - all other geometries will violate cosmological principle by not being homogeneous or isotropic.

CMB and red shift is pretty much proof that things will indeed look like they are receding "faster than the speed of light", but there will never ever be direct proof for that - simply by the virtue that if something is moving with speed faster than the speed of light - it is in causally disconnected part of universe - no "measurement" will ever reach us from that object - it is as if such thing vanished out of existence.

It's a bit like asking if we can prove that light indeed can't escape black hole - how to do it? But we do know black holes exist - there is a lot of evidence for their existence and this evidence supports what we know of these objects and how they behave.

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The current view of physical theories is that they hold in a specific range of applicability.

This is often related to energy in one way or another.

Newtons theory of gravity is correct in flat space-time but fails when the curvature due to gravity (stress energy) gets too large. General relativity fails at small scales (or so its thought but we have no evidence one way or the other). Quantum mechanics seems to require a high energy cut off to avoid the UV catastrophe in renormalistaiom. The standard model of particle physics is expected to fail just beyond the energy range of the LHC!

Given the limited range of energies available to us we have theories that work for all practical purposes but are expected to fail in some more extreme circumstances.

Regards Andrew

Edited by andrew s
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All good mind-bending stuff!

So, let me see if I've got this right -

the edge of the "observable" universe is around 13.8 bill l.y. away (radius of the observable universe). This is an horizon created by the age of the universe since recombination, and the CMB light was released, and not the true "edge" of the universe (if indeed there is an edge).  In the time the light has been travelling to us, the universe has continued to expand, and the bits we currently see at the "edge" are actually not 13.8 billion ly away, but some number much bigger than this.

The observable universe is just "our" observable universe. To aliens that inhabit a world billions of light years away, they will have there own observable universe and will be able to see objects that we cannot, because they lie outside of our horizon.

Is this broadly correct (assuming cosmological theory is correct of course!)

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2 hours ago, vlaiv said:

You mention edges of universe - there is no such thing. Space expands at a certain rate, currently at about 70km/s per Mpc - meaning for each mega parsec of distance rate of expansion of universe is such that object will be moving away from us at about 70km/s (67km/s or 73km/s - depending on data used to calculate - one of problems in modern cosmology).

This is rate of expansion between us an our neighboring galaxies as well as rate of expansion between galaxies billion light years away (local rate of expansion). Space expands at that rate "all over the place" and this rate of expansion is governed by all the "stuff" in universe (meaning energy in different form - matter, light, vacuum). We can't say that space is expanding faster than light. What we can say instead is that two objects - far enough, look like they are "receding" from each other at speed greater than the speed of light. In fact this is what is causing horizon that we experience. Space is probably many times larger than our observable universe - our measurements lack precision to determine this yet. As far as we know, our universe is flat within 1% of uncertainty of measurement. This could simply mean that it's positively curved (or negatively) with very large radius. If you were to measure curvature of earth on 1km squared patch of desert with meter stick - you would have no idea that you are on spherical object - thing would look flat to you.

So we have no idea if space is indeed flat and infinite (or maybe finite in extent but without bounds - violating our assumption of isotropy), positively curved with finite radius (and again no boundary), negatively curved and infinite, ....

There is one great assumption in place when we discuss cosmology - that is cosmological principle. It's our assumption that we are in isotropic and homogeneous universe, and that we hold no special position in it - extension of Copernican principle.

If we go by above principle, then there are only three geometries that fit - flat and infinite (euclidean space), negatively curved and infinite (hyperbolic geometry) and positively curved and finite (3 sphere) - all other geometries will violate cosmological principle by not being homogeneous or isotropic.

CMB and red shift is pretty much proof that things will indeed look like they are receding "faster than the speed of light", but there will never ever be direct proof for that - simply by the virtue that if something is moving with speed faster than the speed of light - it is in causally disconnected part of universe - no "measurement" will ever reach us from that object - it is as if such thing vanished out of existence.

It's a bit like asking if we can prove that light indeed can't escape black hole - how to do it? But we do know black holes exist - there is a lot of evidence for their existence and this evidence supports what we know of these objects and how they behave.

Thanks Vlaviv, I enjoy each post of yours  like a good sci book!

Unfortunately, I am in a lack of knowledge and it pushes me to be "believer" than "I actually know" person,  -  I am a very bad believer... in all aspects of life...

And I keep a very skeptical view even on scientific explanations which contradicts logic and even it's own statements.
Like: "all" started from "little" nothing and expands/falls into nothing, we do not know what nothing is and if nothing can exist at all.

That "thing" which expands into all directions we look at, is actually flat and it has no center there expansion/falling started from, plus nothing cannot fall/move faster than speed of light as the time and "the thing" will adjust itself to keep the speed constant, except, - from the mater which is on that "thing" which falls/expands into opposite directions on other parts of universe.

Plus, quantum entanglement... based on that, all particles should be entangled as they been "born" from the same "something", but their are not...

I simply can kill my brain trying to understand how all That can fit into formulas correctly.

Sadly my lack of knowledge makes me a bad partner for disputes in this field

Edited by RolandKol

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12 minutes ago, Astrokev said:

All good mind-bending stuff!

So, let me see if I've got this right -

the edge of the "observable" universe is around 13.8 bill l.y. away (radius of the observable universe). This is an horizon created by the age of the universe since recombination, and the CMB light was released, and not the true "edge" of the universe (if indeed there is an edge).  In the time the light has been travelling to us, the universe has continued to expand, and the bits we currently see at the "edge" are actually not 13.8 billion ly away, but some number much bigger than this.

The observable universe is just "our" observable universe. To aliens that inhabit a world billions of light years away, they will have there own observable universe and will be able to see objects that we cannot, because they lie outside of our horizon.

Is this broadly correct (assuming cosmological theory is correct of course!)

Yes.

Current accepted theory is that the Universe is spatially flat and always has been.

Regards Andrew

Edited by andrew s

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Nope....

Observable Universe is much larger than 13.8bil L.Years radius
this is another "thingy"....

Odd one

Edited by RolandKol

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26 minutes ago, RolandKol said:

Nope....

Observable Universe is much larger than 13.8bil L.Years radius
this is another "thingy"....

Odd one

Can you explain why you say the observable universe is larger?

in my understanding, by "observable" we are talking about what we can actually see, which I believe is out to 13.8bil ly. This "edge" is, right now, much farther away than this, but we cannot see it and therefore it is not "observable". We are currently viewing where it is as it was 13.8bil years ago, not where it is now.

Maybe we saying the same thing but getting caught up on the language? It's very easy to introduce ambiguity with all of this!

Edited by Astrokev

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33 minutes ago, andrew s said:

Yes.

Current accepted theory is that the Universe is spatially flat and always has been.

Regards Andrew

Not sure if this is the case. Current accepted theory does not put constraint on geometry of universe, and there are three distinct possibilities - K=-1, 0 and 1.

For simplest case of 6 parameter lambda CDM model, it is assumed that K is 0 and Plank data gives current measurement of ΩK, to be 0.000±0.005. This puts lower bound of curvature radius in cases of positive and negative curvature but it does not tell us if space is indeed positively, negatively or zero curved.

38 minutes ago, RolandKol said:

Nope....

Observable Universe is much larger than 13.8bil L.Years radius
this is another "thingy"....

Odd one

Nope ...

Observable universe is indeed of 13.8Bly radius if you describe distances by light-travel measure.

There are different ways to measure distance in expanding universe. One of those measures - light-travel measure is straight forward, and in that measure light indeed needed to travel for 13.8 billion years traveling at light speed to cross the distance needed to reach us.

Then there is co-moving distance - that one gives radius of about 46Bly. This one should be read as - if you had a long enough ruler and place it in universe now - point that emitted light that traveled 13.8By at speed of light and covered 13.8Bly would sit at 46Bly on that ruler.

This is precisely due to expanding universe. If we take a point in time where photon emitted is still traveling to us, and is about half way between origin and us - for remaining travel time both space "behind" the photon and "in front" of the photon will stretch as photon is "flying". This is why "physical" distance is 46Bly while photon only traveled 13.8Bly - other distance comes from stretching of space (actually some photon travel distance also comes from stretching - as space "in front" of photon is still stretching as photon "flies"

For different distance measures used in cosmology look here:

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9 minutes ago, vlaiv said:

Not sure if this is the case. Current accepted theory does not put constraint on geometry of universe, and there are three distinct possibilities - K=-1, 0 and 1.

For simplest case of 6 parameter lambda CDM model, it is assumed that K is 0 and Plank data gives current measurement of ΩK, to be 0.000±0.005. This puts lower bound of curvature radius in cases of positive and negative curvature but it does not tell us if space is indeed positively, negatively or zero curved.

My understanding is that it is taken to be zero  in the LCDM concordance model and hence has been and always will be zero.  This implies it is spatially infinite.

The difficulty with the zero is that there will always be error bars which leave some wiggle room.

Regards Andrew

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1 hour ago, vlaiv said:

Not sure if this is the case. Current accepted theory does not put constraint on geometry of universe, and there are three distinct possibilities - K=-1, 0 and 1.

For simplest case of 6 parameter lambda CDM model, it is assumed that K is 0 and Plank data gives current measurement of ΩK, to be 0.000±0.005. This puts lower bound of curvature radius in cases of positive and negative curvature but it does not tell us if space is indeed positively, negatively or zero curved.

Nope ...

Observable universe is indeed of 13.8Bly radius if you describe distances by light-travel measure.

There are different ways to measure distance in expanding universe. One of those measures - light-travel measure is straight forward, and in that measure light indeed needed to travel for 13.8 billion years traveling at light speed to cross the distance needed to reach us.

Then there is co-moving distance - that one gives radius of about 46Bly. This one should be read as - if you had a long enough ruler and place it in universe now - point that emitted light that traveled 13.8By at speed of light and covered 13.8Bly would sit at 46Bly ﻿on that ruler.

This is precisely due to expanding universe. If we take a point in time where photon emitted is still traveling to us, and is about half way between origin and us - for remaining travel time both space "behind" the photon and "in front" of the photon will stretch as photon is "flying". This is why "physical" distance is 46Bly while photon only traveled 13.8Bly - other distance comes from stretching of space (actually some photon travel distance also comes from stretching - as space "in front" of photon is still stretching as photon "flies"

For different distance measures used in cosmology look here:

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