# What is the current radius of the observable universe?

## How big is the observable universe (assuming age is 14 billion years)

• ### [8)] none of the above

• Total voters
11
S

I see.
so if space is expanding like H = dr/rdt then the R in the present moment would be R=Roev/c ?

#### marcus

Gold Member
Dearly Missed
I see.
so if space is expanding like H = dr/rdt then the R in the present moment would be R=Roev/c ?
Hello "2GM/c2"

Would it be all right to use the letter D to stand for the
distance to some object, like a galaxy?

I am used to seeing the Hubble law written v=H0D

the subscript zero means "value at the present time"
v is the comoving radial velocity at present
D is the distance at present (must be the comoving distance not the light travel time distance, for the law to be valid)

I am used to seeing R, in these contexts, meaning not the distance to an object but a scale factor that goes into the metric or that indicates "average distance between galaxies".
It serves as an index of the size of the universe (since the universe is infinite one needs some spacing index like average distance between galaxies) to keep track of the expansion.
R0 is the PRESENT value of this size indicator.

And the "a" that one sees in the Friedmann eqns. is a dimensionless version of R, namely R/R0 .

You divide past and future R by the present value and get a number which at the present is one. Then the Friedmann equations take on their usual textbook form.

Is this notation OK with you? Or would you like to use R to be the distance to some object?

Anyway, if I stick to what I'm familiar with for the moment, the Hubble law is v= H0 D, and that (not what you wrote) is the way that current velocity and current distance of objects are related. It is a simple linear relation which is kind of a relief, and (as Wright say) it holds for all distances.

(forgetting about proper motion, which at large redshifts is a small part, just a sort of random fuzz, compared with the main speed of expansion of space)

L

#### LogicalAtheist

Marcus - It's unfortunate no one here was able to give you the answer to your question "what is the current radius of the universe".

The answer is: 4 x 10^26 meters

There you have it.

#### marcus

Gold Member
Dearly Missed
Originally posted by LogicalAtheist
Marcus - It's unfortunate no one here was able to give you the answer to your question "what is the current radius of the universe".

The answer is: 4 x 10^26 meters

There you have it.
This is a charming answer. I am used to thinking of such distances in LY so let me convert your 4E26 meters.

Hmmm a LY is 9.46E15 meters, so you are saying.....

Ye gods and little fishes! You are saying

FORTY TWO BILLION LIGHT YEARS!!!!

YES!!!! Measured at the present moment from perspectives at rest relative to the Cosmic Microwave Background, this is indeed the upper limit on the distance of the farthest detectable sources. this is the radius of the observable universe at present.

Tell me how to become an atheist. I will join your church
I am glad to have met you.

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#### heusdens

Again this question, on which I heard opposing views.

Our visible universe is known to expand. The question I have is wether this expanding buble of space, that denotes our horizon of vision, always "contains" (that is: visible at some specific point in time, cause the light reaches us) the same amount of matter.
Or in other words, does this expanding bubble as it grows in the course of time show us more galaxies and stars then in the past, or quit opposite, galaxies and stars that were visible once, escape from our horizon, cause they recede from us at speeds > c?

#### marcus

Gold Member
Dearly Missed
This is an excellent question to have thought to ask.
The future contents of the observable universe depend on what model one choses. Soon after "dark energy" and "accelerating expansion" became popular topics (1998) cosmologists began to point out that with accelerating expansion after a while the observable universe might have only a hundred or so galaxies in it----we would get lonely in other words.

One must be mentally prepared for the expansion rate to change and even to reverse. If the universe begins to contract at some time in the future---a logical possibility---the "bubble" as you call it would get very full of matter and radiation---we would have too much company.

That said, I can answer your question under the simplifying assumption of a flat universe with no cosmological constant (zero "dark energy")----by far the simplest model and until recently the most realistic and widely assumed.

Orthodox cosmologists use a special idea of rest frame---that of an observer at rest with respect to the expansion of the universe---also called the "Hubble flow" (just another name for uniform expansion)----which means at rest with respect to the CMB.

They use the distance definition, and the idea of simultaneity, which belongs to this rest frame. The distance is measured at the present instant of time and is called the "comoving distance".
For an unmathematical but careful definition look in Wright's Cosmology tutorial.

A feature of the tutorial called the Cosmological Calculator will find the comoving distance to things given the redshift in their most recent observation. So if a quasar is observed with redshift z = 6.4 the calculator will tell you the current comoving distance to it.

This is about 27 billion LY, as I recall. Space around that particular quasar is currently receding at about 2c. (This is the standard Hubble law v = H0 D, interpreted in the normal way that cosmologists use the law. Widely misunderstood by outsiders unfortunately.)

Originally posted by heusdens
The question I have is wether this expanding buble of space, that denotes our horizon of vision, always "contains" (that is: visible at some specific point in time, cause the light reaches us) the same amount of matter.
No it does not!

Originally posted by heusdens

Or in other words, does this expanding bubble as it grows in the course of time show us more galaxies and stars then in the past?

Yes! under the simple assumptions about the expansion which i stated.

I have to go, but will get back for more discussion later. Here for reference is your complete post.

Originally posted by heusdens
Again this question, on which I heard opposing views.

Our visible universe is known to expand. The question I have is wether this expanding buble of space, that denotes our horizon of vision, always "contains" (that is: visible at some specific point in time, cause the light reaches us) the same amount of matter.
Or in other words, does this expanding bubble as it grows in the course of time show us more galaxies and stars then in the past, or quit opposite, galaxies and stars that were visible once, escape from our horizon, cause they recede from us at speeds > c?

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#### marcus

Gold Member
Dearly Missed
a picture of what I'm describing

http://www.astro.ucla.edu/~wright/cosmo_03.htm

and scroll down the page till you come to the paragraph
"Manipulating Space-Time Diagrams"

You will see a picture of our past light-cone
in the "flat" (critical density) zero-Lambda case.
It is a good approximation even though the dark energy term is zero

In the spacetime diagram the observable universe is
PEAR SHAPED going back to the beginning of time.

I am not saying to browse Wright's Tutorial (which you probably already have done, like everybody else I know)
I am pointing to a particular spacetime diagram in a specific paragraph on page 3.

The age of the univere in that diagram is 8 units (these would be units of 1.7 billion years).

You can see the world lines of the other galaxies in it and you can see if you redrew the PEAR for an age of 7 time units it would be a smaller pear and would contain fewer other galaxies!

this shows that the observable universe actually contains more matter as time goes on.

This is not an obvious conclusion but depends on assumptions about the model, so it is a good thing to be asking about.

#### heusdens

Re: a picture of what I'm describing

Originally posted by marcus

http://www.astro.ucla.edu/~wright/cosmo_03.htm

and scroll down the page till you come to the paragraph
"Manipulating Space-Time Diagrams"

You will see a picture of our past light-cone
in the "flat" (critical density) zero-Lambda case.
It is a good approximation even though the dark energy term is zero

In the spacetime diagram the observable universe is
PEAR SHAPED going back to the beginning of time.

I am not saying to browse Wright's Tutorial (which you probably already have done, like everybody else I know)
I am pointing to a particular spacetime diagram in a specific paragraph on page 3.

The age of the univere in that diagram is 8 units (these would be units of 1.7 billion years).

You can see the world lines of the other galaxies in it and you can see if you redrew the PEAR for an age of 7 time units it would be a smaller pear and would contain fewer other galaxies!

this shows that the observable universe actually contains more matter as time goes on.

This is not an obvious conclusion but depends on assumptions about the model, so it is a good thing to be asking about.
This conclusion, followed from this line of thought, I was already aware of. But I ask the question, cause one could think of another line of thought, which implements the opposite, namely because of the fact that the "recession speed" can be bigger then c, which would mean that at some time, far remote objects move out of our horizon.

Is this a valid representation and conclusion, based on the fact that very far remote objects in principle can have recession speeds bigger then c?

#### heusdens

Length unit

And here is another issue, related to measuring on larger scale size.

First we denote the fact that from GR it can be stated that space is "expanding" in all parts of space. We do not know exactly the amount of space expansion throughout history (it is asummed now, that the expansion in fact accelerates!), but the assumption is that the rate of expansion at any given time (as measured relative to the Big Bang) is constant throughout space.

The fact that we claim that space expands, is a fact which is based on the choice of measuring unit. The measuring unit we have are based on some fundamental constants (I heard it can be expressed using constants of c, h and perhaps G). In principle thought the choice of the length unit is arbitrary. Of course, anyone agrees that if the length unit would expressed differently, this would not alter any of the physical phenomena and laws, it would just alter numerical results.

But how arbitray is the choice of measuring units? We can of course think of choices of length units, which are wrong. As an example, the distance between earth and the sun, would not be a good candidate for the length unit. Since we know from the old measuring units, that the distance between the earth and the sun is not constant. If we choose this distance as the length unit, this would then mean the distance between earth and the sun would be constant. But at the same time, the radius of earth and all other objects known to us, would also vary in time, in a periodically way. No known laws of physics could explain this fact, and that just means this choice of measuring unit is invalid.

But what if our length unit would be choosen in such a way, that it does express some fundamental property of nature. As I suggest, the expansion of space itself, could be a derivate for such a length unit. The choice would then be to denote this measuring unit in such a way, as to effectively "remove" the space expansion. The unit of length could be defined as the distance in space of two very distantiated objects, which both are "stationary" in respect to the CMBR (from the anisotropy of the CMBR we can for instance measure our speed and direction relative to the CMBR). Although this length unit would by no means be practical (which in itself is not a problem, but just requires to properly rescale the unit) it also would mean a totally different perspective on physical phenomena and physical law. For instance the phenomena of "space expansion" would not be a phenomena any more. On the other hand, this "new physics" would have to deal with explaining why all material objects (galaxies, stars, atoms, etc) are contracting in the course of time.

As can be stated all other measuring units (time, mass, etc) would also "behave differenly" in this new measuring unit system, and it would effect also the universal constants, of which some might not be a constant.

The only way this idea for a new measuring unit, which is porportional in time with the expansion of space (effectively cancelling the space expansion phenomena), can be invalidated is to state that the length units we currently have, denote fundamental properties of nature, are expressed in universal constants which are known not to change.

But so far as I can understand physcial law myself, the notion of the universal constants, are assumptions, which - although the reasons for stating that they are constants are strong - do not have to conform reality. For instance the value of h, G or even c in the far past could have been different values as now.

Some theoretical physicist in fact are playing with the thought that some fundamental constant might not be fundamental constants alltogether, and which also gives rise to the idea that perhaps in different frames of reference, we need to apply different measuring units. This is for instance the case with the idea of 'Double Relativity' (see https://www.physicsforums.com/showthread.php?s=&threadid=1465").

Although these ideas are not the same as my idea/proposal for redefining the length unit, and with that effectively 'create' a new physcics, alongside with the old physics, it sure means that our current way in which we define measuring units and universal constants, might not be the only way, and might not even be the right way.

My idea about this new length unit, I have not yet thought through completely. It for sure involves a lot, because we need to redefine all of our measuring units, and it would change a lot in our perspective of the universe (notions as 'age' and 'size' of (observable) universe would be quite different) and would urge us to state that all such notions, basically are not in any way fundamental notions, but relative notions (they depend on the choices of measuring unit).
For instance, in the new measuring unit system, since there is no expansion of space, neither a 'Big Bang' phenomena happened, and the age of the universe would be the infinite past.
This can be argued, because when we calculate back to the 'normal' length and time measuring units, the new length and time units (taking speed of light as a constant in the NEW measuring unit system!) would both be expanding in time, which means that further to the past, both measuring units were shorter. So in new time units, the time between now and the big bang denote an infinite amount of time. In effect it would mean that all our references to these things (like the age of the universe) can not be taken as 'absolute' notions, but only 'relative' notions, since it depends on the choise of measuring units.

Perhaps this new vision, based on this new measuring unit for length, is arguably wrong, but as far I have not seen fundamental arguments against it. For instance the argument that the choice of a measuring unit that increases in size in the course of time, is an invalid option, is a way of circular reasoning. Because wether or not something increases in size, is always based on the choice of measuring unit. Based on the new measuring unit, it could be stated that this is not the case, but that our normal measuring unit is shrinking in size. Based on that argument, we could only tell that one of them needed to be incorrect, but we could not tell which one was incorrect.

So the argument then basically comes down to claim that the chosen measuring unit is absolute, and expresses a fundamental property of nature. And of course, that is dependend on some universal properties, which in our measuring units, denote some constants.
But from what do we know that?

I think we can not make any ABSOLUTE claim about that. Which then would lead to the thought that both measuring unit systems have equal validity, even when we know that physical laws and physical phenomena are not identical in both measuring unit systems.

This idea can be thought of as an extention to the theory of relativity, in which not only all measurements are relative, but also the measuring units themselves are relative.

Since most of the time our physical explenations and phenomena we deal with, are on much smaller time and lenth scales as that of the universe, there is of course no reason to leave our normal measuring unit systems and understanding and interpretation thereof.
But for cosmological issues, the new measuring unit system could be a progressive step forwars in understanding the universe.

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#### marcus

Gold Member
Dearly Missed
Hi heusdens, it is a nice try but doesnt work

I am replying to what you said in previous post:
"But what if our length unit would be choosen in such a way, that it does express some fundamental property of nature. As I suggest, the expansion of space itself, ...."

You have been given a bad misconception from popular accounts and the careless way astronomers talk

The rate that space is expanding is different in different places.
It is uneven.
Uniform expansion is not at all a "fundamental property" of space built into its nature.

When they talk about the expansion rate they mean a kind of temporary average.
The average is only strictly correct for the present moment (t=0) which is why they write the zero subscript on H0.

And it is only a rough estimate gotten by averaging the expansion in various places and directions from us, which rigorously speaking are all different.

The main equations of cosmology---Friedmann's two equations---are boiled down from Einsteins by ASSUMING that the distribution of energy in space is isotropic and homogeneous (same everywhere and in all directions) which it obviously is NOT.

However the Friedmann equations are simple and terribly useful and the work soooooo well! Even though predicated on obviously false assumptions. These equations contain the definition of the Hubble constant----the idealized expansion rate.

We have enough to worry about with the fundamental constants we already have. Please do not suggest that the expansion-rate of space is also a "fundamental constant"!
Compared with other things it is highly changeable.
One should really call it "Hubble parameter" (as some people are starting to do) and not call it Hubble "constant."

But cheers anyway, I sympathize with your interest in scales of measurement and foundations-issues

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#### heusdens

Originally posted by marcus
Hi heusdens, it is a nice try but doesnt work

I am replying to what you said in previous post:
"But what if our length unit would be choosen in such a way, that it does express some fundamental property of nature. As I suggest, the expansion of space itself, ...."

You have been given a bad misconception from popular accounts and the careless way astronomers talk

The rate that space is expanding is different in different places.
It is uneven.
Uniform expansion is not at all a "fundamental property" of space built into its nature.

When they talk about the expansion rate they mean a kind of temporary average.
The average is only strictly correct for the present moment (t=0) which is why they write the zero subscript on H0.

And it is only a rough estimate gotten by averaging the expansion in various places and directions from us, which rigorously speaking are all different.

The main equations of cosmology---Friedmann's two equations---are boiled down from Einsteins by ASSUMING that the distribution of energy in space is isotropic and homogeneous (same everywhere and in all directions) which it obviously is NOT.

However the Friedmann equations are simple and terribly useful and the work soooooo well! Even though predicated on obviously false assumptions. These equations contain the definition of the Hubble constant----the idealized expansion rate.

We have enough to worry about with the fundamental constants we already have. Please do not suggest that the expansion-rate of space is also a "fundamental constant"!
Compared with other things it is highly changeable.
One should really call it "Hubble parameter" (as some people are starting to do) and not call it Hubble "constant."

But cheers anyway, I sympathize with your interest in scales of measurement and foundations-issues
That's a good point!

And there is one other thing about the Hubble correlation parameter.
We can only observe this correlation in a very tiny spatial and temporal extent (namely: the temporal and spatial extend in which we know about, or since we do scientific cosmologic observations).

How do we know then that there is a distance - velocity ("virtual" recession speed) relation, it could as well be a time - velocity / virt. reces. speed relation.

#### meteor

For me, the answer is 14 billion y.l. And look what says Alan Guth, the creator of the theory of inflation:
"We find that the universe is expected to be at least 10 to the power of 23 times larger than the observed universe. If the inflationary theory is correct, then the observed universe is only a minute speck in a universe that is many orders of magnitude larger"

#### heusdens

Originally posted by meteor
For me, the answer is 14 billion y.l. And look what says Alan Guth, the creator of the theory of inflation:
"We find that the universe is expected to be at least 10 to the power of 23 times larger than the observed universe. If the inflationary theory is correct, then the observed universe is only a minute speck in a universe that is many orders of magnitude larger"
Alan Guth worked out his own version of what is called inflation, based on an idea of the Soviet scientist Starobinsky, end of the '70-ies. This model, about a large scale transformation of matter in the universe, was however too complicated, and in fact did not work.
But it has lead to new attempts, for instance by Alan Guth and others. There have appeared a number of ideas in that field, for instance that of eternal / chaotic / open inflation by Andrei Linde.

#### Michael F. Dmitriyev

All contradictions withdraws if take as a basis the law of conservation of Time Cycle of objects (universe in particular). In this case the universe can enlarges, in the same way can compresses. These phenomenas can be as global , in the same way can be as local. It is possible to present universe as a complex system with automatic regulation.

"What is the current radius of the observable universe?"

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