How does the expansion of space affect the age of the universe?

[yazanhomsi]

Hello everyone!

I've been having trouble regarding the age of the universe and another small problem. This problem escalated when I first started reading Dr. Brian Greene's book "The Hidden Reality". The distinction between the two possibilities, that our universe is finite or infinite, plays no role in the age of the universe. In his book, on pages 27-28, Dr. Greene states the following:

"In an infinite universe, most regions lie beyond our ability to see, even using the most powerful telescopes possible. Although light travels enormously quickly, if an object is sufficiently distant, then the light it emits - even light that may have been emitted shortly after the big bang - will simply not have had sufficient time to reach us. Since the universe is about 13.7 billion years old, you might think that anything farther away than 13.7 billion light-years would fall into this category. The reasoning behind this intuition is right on target, but the expansion of space increases the distance to objects whose light has long been traveling and has only just been received; so the maximum distance we can see is actually longer - about 41 billion light-years. But the exact numbers hardly matter. The important point is that regions of the universe beyond a certain distance are regions currently beyond our observational reach. Much as ships that have sailed beyond the horizon are not visible to someone standing on shore, astronomers say that objects in space that are too far away to be seen lie beyond our cosmic horizon."

Can someone please explain this in details for me? Like how do we know the age of the universe? We know how old it is but we do not know how far away the big bang is because our telescopes cannot see it (beyond our cosmic horizon). Since the 13.7 billion light-years now became 41 billion light-years, doesn't that mean our universe is 41 billion light-years old? I just need a detailed explanation for all of this.

Thank you so much, in advance.

 

[mfb]

The big bang did not happen at some point in space - space didn't exist before. It does not make sense to ask for a distance to the big bang. The hot dense state directly after the big bang was everywhere. The only "distance" it has is a distance in time: 13.7 billion years ago.

Like how do we know the age of the universe?

We can observe how fast space expands now and how fast it did in the past, which allows to calculate back to the point where the universe started (where the size was "zero"). There are more methods, but that is the basic idea.

Since the 13.7 billion light-years now became 41 billion light-years, doesn't that mean our universe is 41 billion light-years old?

No. Why should it make the universe older if things move away from us? Also, there are no 13.7 billion light years. 13.7 billion years ago, all matter everywhere emitted light. The light of things nearby reached "us" quickly, the light from things about 40 million (!) light years away back then is reaching us now, the light from things 41 million light years away will reach us in about a billion years. Distances expanded by a factor of about 1100 since then, so the matter discussed here (where the 13.7 billion year old light is reaching us now) is now about 44 billion light years away. The difference to the number of 41 given above comes from measurement uncertainties and rounding errors.

 

[yazanhomsi]

The big bang did not happen at some point in space - space didn't exist before. It does not make sense to ask for a distance to the big bang. The hot dense state directly after the big bang was everywhere. The only "distance" it has is a distance in time: 13.7 billion years ago.

We can observe how fast space expands now and how fast it did in the past, which allows to calculate back to the point where the universe started (where the size was "zero"). There are more methods, but that is the basic idea.

No. Why should it make the universe older if things move away from us? Also, there are no 13.7 billion light years. 13.7 billion years ago, all matter everywhere emitted light. The light of things nearby reached "us" quickly, the light from things about 40 million (!) light years away back then is reaching us now, the light from things 41 million light years away will reach us in about a billion years. Distances expanded by a factor of about 1100 since then, so the matter discussed here (where the 13.7 billion year old light is reaching us now) is now about 44 billion light years away. The difference to the number of 41 given above comes from measurement uncertainties and rounding errors.

Alright I kind of understand now what you said. Just to check if I get it. So the universe is 13.7 billion years old, which means light that reaches us NOW has traveled 13.7 billion light years. So the light that will reach us in 27.3 billion years (if we are still alive) would have traveled 41 billion light years, making our universe 41 billion years old? Is that correct, if so then yes I get exactly what you said.

 

[Mordred]

Alright I kind of understand now what you said. Just to check if I get it. So the universe is 13.7 billion years old, which means light that reaches us NOW has traveled 13.7 billion light years. So the light that will reach us in 27.3 billion years (if we are still alive) would have traveled 41 billion light years, making our universe 41 billion years old? Is that correct, if so then yes I get exactly what you said.

No this isn't correct, the universe is roughly 13.7 billion years old but the size of the observable universe is roughly 46 Gly, The reason light can reach us across this distance is due to the expansion of the universe.

Here is a simple exercise. Take a graph paper. Start at the center column. Set emitter a 4 columns left of center. Observer b 4 columns right of center. Label each row year 1a and 1b respectively. Set travel distance light can cross in one year to 1 cm.

Draw 1 cm from a to b.= year one. Label the right end as 1c.

For year two draw a line down column 5 from center, left and column 5 right from center. This is expansion in 1 year. Label this 2A and 2b respectively. Draw a vertical line from 1c end point of where light traveled in year one onto second year row, then measure 1 cm to right from that point, on year two. Label it 2c

Repeat the steps above as often as needed. You can see that BOTH the distance behind and in front of the light Ray increases.

( The units are not to scale, its just a visual aid to see how light can travel farther than 13.7 GLY, due to universe expansion.

 

[Bandersnatch]

No this isn't correct

Hi Mordred. I think the OP meant that in a universe of 41 billion years we'd see light with light travel time of 41 billion years, in the same way as in a universe of 13.7 Gy we see light (CMBR) that has traveled for 13.7 Gy.
Which is correct, isn't it?

 

[Mordred]

Hi Mordred. I think the OP meant that in a universe of 41 billion years we'd see light with light travel time of 41 billion years, in the same way as in a universe of 13.7 Gy we see light (CMBR) that has traveled for 13.7 Gy.
Which is correct, isn't it?

Yeah I may have misread, his post. He wasn't specifying distance of travel, now that I read it again. Ah well it's still an informative exercise lok

 

[yazanhomsi]

Y

Hi Mordred. I think the OP meant that in a universe of 41 billion years we'd see light with light travel time of 41 billion years, in the same way as in a universe of 13.7 Gy we see light (CMBR) that has traveled for 13.7 Gy.
Which is correct, isn't it?

yep that is what i meant thank you

 

[yazanhomsi]

No this isn't correct, the universe is roughly 13.7 billion years old but the size of the observable universe is roughly 46 Gly, The reason light can reach us across this distance is due to the expansion of the universe.

Here is a simple exercise. Take a graph paper. Start at the center column. Set emitter a 4 columns left of center. Observer b 4 columns right of center. Label each row year 1a and 1b respectively. Set travel distance light can cross in one year to 1 cm.

Draw 1 cm from a to b.= year one. Label the right end as 1c.

For year two draw a line down column 5 from center, left and column 5 right from center. This is expansion in 1 year. Label this 2A and 2b respectively. Draw a vertical line from 1c end point of where light traveled in year one onto second year row, then measure 1 cm to right from that point, on year two. Label it 2c

Repeat the steps above as often as needed. You can see that BOTH the distance behind and in front of the light Ray increases.

( The units are not to scale, its just a visual aid to see how light can travel farther than 13.7 GLY, due to universe expansion.

Thank you for the exercise it really helped anyway to increase my information

 

[PeterDonis]

I think the OP meant that in a universe of 41 billion years we'd see light with light travel time of 41 billion years

I think the OP's question was confused. He's mixing up three different things: light travel time; the distance the light has traveled; and the distance between the emitter of the light and us receiving it. See below.

the universe is 13.7 billion years old

Yes.

which means light that reaches us NOW has traveled 13.7 billion light years

No. You are trying to apply intuitions that don't work in an expanding universe.

Let me describe in more detail what happened to light emitted 13.7 billion years ago that is just reaching us now. For simplicity, I'll assume the "light" is actually CMB radiation, because it gives a nice round number for how much the universe has expanded since then. The CMB radiation was emitted when the universe was about 300,000 years old, so it was emitted 13.7 billion years ago to very good accuracy. (Also, light emitted any earlier would not reach us anyway because the universe was not transparent to light until the time of CMB emission.)

At the time of CMB emission, a point in the universe that emitted CMB light that we, on Earth, are just receiving now (call this point P) was about 46 million light-years away from where Earth would have been if it had existed at that time (obviously it didn't, but we can trace back the spatial position of the Earth to that time).

At the current instant of time, 13.7 billion years from the time of CMB emission, when we are just receiving CMB light emitted from point P, point P itself is about 46 billion light-years away from Earth. That is because the universe has expanded by a factor of about 1000 since the time of CMB emission.

What happened in between was two things: the light emitted from point P in the direction of Earth traveled towards Earth; and the universe expanded. The two effects worked against each other; you can think of it, heuristically, as the light having to "swim upstream" against the universe's expansion in order to reach Earth. That's why the travel time of the light is not equal to either the time it would take light to travel the distance between P and Earth at the time of CMB emission (46 million years) or the time it would take light to travel the distance now between P and Earth (46 billion years), but something in between (13.7 billion years).

As for what distance the light "actually" traveled, there isn't really a well-defined answer. In an expanding universe, "distance" only has meaning at a single instant of time; for objects that take a lot of time to travel, there is no unique way to tell what distance they have traveled. The only really meaningful quantity is the travel time.

What I'm saying here is basically the same as what Mordred said, I just used different words.

 

[yazanhomsi]

Alright I get everything you said but

That's why the travel time of the light is not equal to either the time it would take light to travel the distance between P and Earth at the time of CMB emission (46 million years) or the time it would take light to travel the distance now between P and Earth (46 billion years), but something in between (13.7 billion years).

Can you re-explain this part please? I am finding difficulties understanding it.

 

[yazanhomsi]

I think the OP's question was confused. He's mixing up three different things: light travel time; the distance the light has traveled; and the distance between the emitter of the light and us receiving it. See below.
Yes.
No. You are trying to apply intuitions that don't work in an expanding universe.

Let me describe in more detail what happened to light emitted 13.7 billion years ago that is just reaching us now. For simplicity, I'll assume the "light" is actually CMB radiation, because it gives a nice round number for how much the universe has expanded since then. The CMB radiation was emitted when the universe was about 300,000 years old, so it was emitted 13.7 billion years ago to very good accuracy. (Also, light emitted any earlier would not reach us anyway because the universe was not transparent to light until the time of CMB emission.)

At the time of CMB emission, a point in the universe that emitted CMB light that we, on Earth, are just receiving now (call this point P) was about 46 million light-years away from where Earth would have been if it had existed at that time (obviously it didn't, but we can trace back the spatial position of the Earth to that time).

At the current instant of time, 13.7 billion years from the time of CMB emission, when we are just receiving CMB light emitted from point P, point P itself is about 46 billion light-years away from Earth. That is because the universe has expanded by a factor of about 1000 since the time of CMB emission.

What happened in between was two things: the light emitted from point P in the direction of Earth traveled towards Earth; and the universe expanded. The two effects worked against each other; you can think of it, heuristically, as the light having to "swim upstream" against the universe's expansion in order to reach Earth. That's why the travel time of the light is not equal to either the time it would take light to travel the distance between P and Earth at the time of CMB emission (46 million years) or the time it would take light to travel the distance now between P and Earth (46 billion years), but something in between (13.7 billion years).

As for what distance the light "actually" traveled, there isn't really a well-defined answer. In an expanding universe, "distance" only has meaning at a single instant of time; for objects that take a lot of time to travel, there is no unique way to tell what distance they have traveled. The only really meaningful quantity is the travel time.

What I'm saying here is basically the same as what Mordred said, I just used different words.

Alright i got it all thanks a lot!

 

[DAH]

The Hubble constant can provide us with a rough value for the age of the universe by using $$\frac{1}{H_o}$$
first you need the correct units for H_o so: $$H_o=\frac{68~km~s^{-1}~Mpc^{-1}}{3.1×10^{19}~km~Mpc^{-1}}=2.19×10^{-18}~s^{-1}$$
So the estimated age is : $$\frac{1}{2.19×10^{-18}~s^{-1}}=4.57×10^{17}~s$$
since 1 year = 3.2 × 10⁷ seconds
then: $$\frac{4.57×10^{17}~s}{3.2×10^{7}~s~y^{-1}}=1.4×10^{10}~y$$
so that's about 14 billion years but this is only an estimate because the Hubble constant has changed slightly since time began.

 

[marcus]

DAH, I would suggest the two curves are not closely matched and just had to cross somewhere. They will cross exactly at some point in the future and then get farther and farther apart.

Here the x-coordinate is the size of distances compared with their present size, so it can substitute for a time coordinate. T is the age of the expansion (or "age of universe") and R = 1/H is the Hubble time. The units are chosen so that in the long term the Hubble time approaches 1 (1 zeit = 17.3 billion years)
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7z/LightConeZ.html
Here's the same plot with vertical scale in billions of years:

According to the best fit cosmic model the exact equality of T = 1/H will occur in only a little more than a billion years from now.

 

[marcus]

IOW for most of the history of the universe 1/H is a bad estimator of the age. There is no physical reason it should be a good estimator. But a clock has to be right ONCE and just by coincidence this is slated to happen some time in the near future . We can even say when it will happen.
Assuming recent measurements of cosmological parameters, it will happen right around year 14.856 billion.

Roughly speaking the exact coincidence will occur in about 1 billion years from now. A little over a billion. But so far we don't know the parameters with such precision that one can be much more definite than that.
$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly) \\ \hline 1.07573&0.92960&14.85538&14.85570\\ \hline 1.07574&0.92959&14.85553&14.85571\\ \hline 1.07575&0.92959&14.85568&14.85573\\ \hline 1.07575&0.92958&14.85582&14.85575\\ \hline 1.07576&0.92957&14.85597&14.85576\\ \hline 1.07577&0.92957&14.85612&14.85578\\ \hline 1.07578&0.92956&14.85627&14.85580\\ \hline 1.07579&0.92955&14.85642&14.85581\\ \hline \end{array}}$$

You can see that with this choice of model parameters the crossing of the curves happens when the scale factor is 1.07575. that is, when distances will be about 7 and 1/2% larger than they are now.

Around that time the "age of the universe" will be something like 14.8557 Gy and the Hubble distance will change from being slightly more than the age, to slightly less.

But it seems pointless to note that because there is no logical connection. Hubble R is not a good estimator of age T, and it's simply a coincidence (according to standard cosmic model) that they should be approaching a crossover point and temporarily be roughly similar in size.

table by Lightcone:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html

 

[amjc]

Hello. I have found an interesting article on this subject, published in Scientific American ( http://www.scientificamerican.com/article/the-universe-s-oldest-stars-were-late-bloomers/ ), which is followed by this comment (signed by "Galileanus"):

"The age of the Universe is 13.8 billion years, the CMB was originated 370,000 years after the big bang, and the reionization occurred 560 million years after the big bang.
These absolute dates for the whole universe, which are consistent with the Big Bang Theory, contradict the concept of relative simultaneity, and also the hypothesis of time dilation (caused by relative motion and gravitational fields). According to Relativity Theory (created by Poincaré and Einstein), an event occurred at the present moment in some place of the Earth cannot be considered simultaneous (in absolute sense) to another event occurred in a distant galaxy, and therefore, there is not an absolute present-date for the whole universe.
In view of this contradiction, it is evident that (at least) one of the two theories (the Relativity or the Big Bang Theory) cannot be true."

… What do you think about this opinion?

 

[Bandersnatch]

Hi amjc

… What do you think about this opinion?

It's misinformed.

Cosmological models use a specific frame of reference to describe evolution of the universe - the only FoR in which the universe looks homogeneous and isotropic. It is not an absolute frame in any sense (consistently with Relativity), but it is a convenient one. All times referred to talk about times measured in this frame of reference. As it happens, we are not traveling at especially high speeds relative to this frame, so all those times are approximately equivalent to temporal separation of events as they'd be measured from Earth.

To put it another way - the fact that I can say that I was born some 30-odd years before I decided to respond to your post, or that my alarm clock rung at 6 AM this morning, does not contradict relativity of simultaneity, even though there is nothing absolute about those events.Furthermore, the poster speaks of Big Bang and Relativity as if they were some completely different theories, whereas BB is a prediction of General Relativity.

Lastly, he calls time dilation a 'hypothesis' as if ignorant of all the experimental evidence accumulated over the last hundred years.

 

[amjc]

Thank you, Bandersnatch, for your answer.

I see that a convenient frame of reference can solve the problem of time dilation, when this is caused by relative motion, and perhaps it solves the relativity of simultaneity …

However, I think that gravitational time dilation does not depend on the reference frame. According to general theory of relativity, time is very slower in the central regions of galaxies (where gravity is very intense), and there are 100 billion galaxies in the observable universe. Therefore, a considerable part of the universe cannot be 13.8 billion years old (in agreement with general relativity), and thus its temperature should be higher, more similar to the initial temperature of the universe.

 

[Bandersnatch]

Cosmological models neglect gravitational time dilation. All times are as as if they were measured far away from any mass concentrations (the universe is treated as if composed of a homogeneous fluid).
But once again, our frame of reference here on Earth is not much different - gravitational fields everywhere but in the closest vicinities of collapsed stars are too weak to factor in significantly.
If the question is whether an observer moving at high speeds through the universe (w/r to the CMBR-rest frame that is used), or orbiting close to a black hole would measure the universe to be of a different age than we do, then the answer is: yes.
But that doesn't change the fact that in the specific, and unambiguous frame of reference we're using the universe has the specified age.

Therefore, a considerable part of the universe cannot be 13.8 billion years old (in agreement with general relativity), and thus its temperature should be higher, more similar to the initial temperature of the universe.

I must say I'm not sure what's the logic behind this.

 

[amjc]

Thank you again.

I mean that, according to big bang theory, the expansion and temperature of the cosmos is a function of time. As the cosmos is older it is more expanded and colder.

However, if the age of the whole universe is not absolute (seeing that the central regions of galaxies should be remarkably younger), this evolution cannot be considered homogeneous.

You say that cosmological models neglect gravitational time dilation and treat the universe as if composed of a homogeneous fluid (… is it more convenient, again?). One can believe, in consequence, that these models are not fully consistent with relativity theory (as Galileanus has claimed).

 

[spacejunkie]

Gravitational time dilation is ignored because it is negligible. It is only non-negligible in highly dense regions. These do not include the centre of the galaxy except the region within a few radii of the black hole event horizon.

 

[mfb]

I see that a convenient frame of reference can solve the problem of time dilation, when this is caused by relative motion, and perhaps it solves the relativity of simultaneity …

There is no problem that would need a solution.

However, I think that gravitational time dilation does not depend on the reference frame. According to general theory of relativity, time is very slower in the central regions of galaxies (where gravity is very intense), and there are 100 billion galaxies in the observable universe. Therefore, a considerable part of the universe cannot be 13.8 billion years old (in agreement with general relativity), and thus its temperature should be higher, more similar to the initial temperature of the universe.

There is an effect, but not in the way you imagined. The CMB temperature does not drop due to time passing, it drops due to the universe expanding. As photons move into gravitational wells or out of them, they gain/lose energy - but in general not the amount they lost/gained before. Those effects are called Sachs–Wolfe effect.

If our galaxy would have existed all the time, and we would have run a clock where the sun orbits, this clock would show a few thousand years less than a clock far away from galaxies. Completely negligible, and with no effect on the CMB temperature anyway.

You say that cosmological models neglect gravitational time dilation and treat the universe as if composed of a homogeneous fluid (… is it more convenient, again?). One can believe, in consequence, that these models are not fully consistent with relativity theory (as Galileanus has claimed).

You cannot conclude that. If you build a house, do you take the gravitational influence of Pluto into account? Of course not. Does that make your model of gravity inconsistent, or just your description of the house not exact?

 

[amjc]

Thank you very much, mfb.

I do not agree or disagree the opinion of that Galileanus, for the moment. I only wanted to clarify these questions on the age of the Universe and its relation with relativity theory (because this is my "Socratic method" of knowledge…)

Now I have found this article ( http://www.space.com/17884-universe-expansion-speed-hubble-constant.html ) on the "speed of Universe’s expansion" and "the expansion rate of the space", which obviously is a function of time (like any other speed or rate), and it is also connected with the decrease of temperature in our Universe after the big bang.

Best regards.

 

[Bandersnatch]

The expansion of the universe is connected to the decrease in temperature of the universe in two ways.
First, the early universe, before structure formation kicked in, was filled with nearly-uniformly distributed plasma. The high homogeneity is apparent in the CMBR. At this stage, due to the lack of defined mass concentrations that could lead to gravitationally-bound regions, the expansion affected the universe throughout its extent. This led to a gradual decrease in density. The plasma acted similar to ideal gas cooling as it was diluted by the expansion. Any considerations of what should happen with temperature of the universe at this stage, and the scale you're talking about, due to gravitational time dilation have no meaning, since there were no regions with high potential difference. The minuscule density fluctuations did cause some regions to cool a tiny fraction later than others, but once again the effect is tiny.

Once the plasma had cooled enough for electrons to combine with nuclei, the CMBR was emitted. This radiation has a spectrum typical of black body at the temperature the universe was at during recombination. As this radiation travels through the expanding universe, its wavelengths get stretched as a result. This translates to the radiation leftover after recombination changing its spectrum to that of a lower-temperature black body. This is the second way temperature is connected to the expansion.
In this sense, high gravitational potential regions again have no bearing on the temperature, since the expansion of the universe does not affect gravitationally-bound regions: all the change in temperature of CMBR you're going to get is from when the radiation traveled through empty space far away from dense mass concentrations like galaxies. It doesn't matter what clocks you use, whether it's some Earth-bound ones, or relatively slower ones orbiting a black hole - you'll observe the same expansion-induced CMBR stretching. You do get blue-shift of the whole radiation as it travels deeper into potential well, but then again you do know how deep in the potential well you are, so it's easy to correct for, making it again unambiguous.

To recapitulate, how deep you are in a potential well has no bearing on the temperature, or the age of the universe you'll calculate, as long as you use the same set of model observers (reference frame).
There's no expansion of the universe in the centres of galaxies that is different from the expansion of the universe elsewhere - there's just no expansion of the universe in the galaxies whatsoever, in the same way as it doesn't affect the solar system or atoms in your body. Once gravitationally-bound, a system is decoupled from the expansion and it evolves according to local interactions.
What is being measured and modeled is the behaviour of the universe on large scales, far away from bound systems (hence why the approximation as continuous fluid is valid).

age of the Universe and its relation with relativity theory

The relation is like so: Einstein field equations -> solution to the field equations -> parameters from observables -> derivables.
The first one is the framework of General Relativity. The second one is the FLRW metric, i.e. expanding/contracting universe, i.e. the Big Bang. The third one is LCDM, i.e. the currently best-fit Lambda-Cold Dark Matter model. The third one includes age.
As you can see, age of the universe and Relativity are not separate, independent ideas, but rather one stems from the other.

 

[wwoollyyhheeaa]

mfb said "No. Why should it make the universe older if things move away from us?" Well it seems to me that when things move away it will take time to do so. This makes the things older. In order to travel from a more distant point to us it takes longer for light to travel. This also makes the things older. Therefore when things move away from us parts of the universe we can still see become older. Is this reasoning illogical? I think I am assuming a universal time and I know that Einstein said this is wrong. But it doesn't have to be wrong.

 

[phinds]

mfb said "No. Why should it make the universe older if things move away from us?" Well it seems to me that when moving away they become further away and it will take time to do so. In order to travel from a more distant point to us it takes longer for light to travel. Therefore when things move away from us parts of the universe we can still see become older. Is this reasoning illogical?

You need to get yourself clear on the definitions of "year" and "light year". You are conflating them in a way that doesn't work.

 

[Drakkith]

mfb said "No. Why should it make the universe older if things move away from us?" Well it seems to me that when things move away it will take time to do so. This makes the things older. In order to travel from a more distant point to us it takes longer for light to travel. This also makes the things older. Therefore when things move away from us parts of the universe we can still see become older. Is this reasoning illogical? I think I am assuming a universal time and I know that Einstein said this is wrong. But it doesn't have to be wrong.

The oldest light we see "now" has been traveling for 13 billion years or so. In those 13 billion years, the emitting objects have moved away from us and are now 46 billion light years away. They aren't 46 billion years old, they've just been moving away from us over time.