How do we know age of the universe?

[yahastu]

Please correct me understanding if it is wrong.

I know that the oldest light we can observe is 13.8 billion light years away.

However, we know that space undergoes inflation, and as a result, there is a maximum observable radius of light that could possibly be seen from any point, regardless of the true size or age of the universe.

Based on the measured rate of space inflation, if we assume it is uniform, it should be possible to calculate what that maximum observable radius is...let's call that R. I assume somebody has calculated this R, although I'm not sure what it would be called.

Obviously R must be greater than or equal to 13.8 billion light years because we have empirical observations going out that far.

If R is greater than 13.8 billion light years, then the fact that we only observe light out to 13.8 billion years would suggest that the universe actually has a radius of only 13.8 billion light years, and that it is 13.8 billion years old...OR that the universe is just locally surrounded by empty space up until the radius of R light years.

On the other hand, if R is exactly equal to 13.8 billion light years, that would suggest that we have no information about the size of the universe save that it must be >= 13.8 billion light years, and that the age must be >= 13.8 billion years. In this situation, to assume that the universe has an edge precisely at the exact distance which happens to be our line of sight sounds like infantile logic -- basically equivalent to the logic of saying that the universe also does not exist in the direction you're not looking.

So, my question is: is R equal to 13.8 billion years, or is R greater than 13.8 billion years, or am I missing something?

 

[Ibix]

I know that the oldest light we can observe is 13.8 billion light years away.

All light we observe is here, otherwise we couldn't observe it. I think you mean that the oldest light we see was emitted 13.8bn years ago.

I think there are two questions here - first, how old is the universe and how do we know, and second how far away are the earliest objects we can see.

The universe is about 13.8bn years old. Essentially we assume that the universe expands uniformly (not "inflates" - inflation refers to what happened in a particular period in our current models of the very early universe), and work out how the redshift would change with distance under different assumptions about the age and density of the universe. Then we see which model best fits our data. That gives us an estimate of the age of the universe.

We can then use that model to identify where an object would have to be to emit light right after the Big Bang so that we receive it now. Then we can carry that position forward to "now" with the expansion of space and see how far away it is. I believe that comes out to about 45bn light years.

So nothing we can see was 13.8bn light years away from us when it emitted light (it was a lot closer), and it is not now 13.8bn light years away (it is a lot further away). And we model the universe as infinite in extent - we just can't ever see the further away bits.

 

[yahastu]

All light we observe is here, otherwise we couldn't observe it. I think you mean that the oldest light we see was emitted 13.8bn years ago.

Yes, that is what I meant

I think there are two questions here - first, how old is the universe and how do we know, and second how far away are the earliest objects we can see.

I can understand why you changed my questions to try to correct for some potential misconceptions, but those aren't really what I was asking...see my bold text below for a better translation of my real question.

The universe is about 13.8bn years old. Essentially we assume that the universe expands uniformly (not "inflates" - inflation refers to what happened in a particular period in our current models of the very early universe),

Why do you differentiate between the words "inflation" and "expansion"? Whether we are talking about the expansion of space that occurred during the first instant, or the expansion of space that continues to occur today, we are still talking about expansion of space...a process that has never ceased, so I don't see the point of calling it two different things now and then.

...and work out how the redshift would change with distance under different assumptions about the age and density of the universe. Then we see which model best fits our data. That gives us an estimate of the age of the universe.

It seems that would only give us an estimate of how long ago the oldest light we can observe was emitted.

However, since we already know that space uniformly inflates or expands, it is obvious that this inflation would prevent us from observing light beyond a certain age -- so therefore we cannot use the maximum age of light that we observe to judge the age of the universe. This is my main point/question that I am trying to understand.

We can then use that model to identify where an object would have to be to emit light right after the Big Bang so that we receive it now. Then we can carry that position forward to "now" with the expansion of space and see how far away it is. I believe that comes out to about 45bn light years. So nothing we can see was 13.8bn light years away from us when it emitted light (it was a lot closer), and it is not now 13.8bn light years away (it is a lot further away). And we model the universe as infinite in extent - we just can't ever see the further away bits.

Makes sense, thanks for that correction

 

[Ibix]

Why do you differentiate between the words "inflation" and "expansion"?

Because inflation is a very rapid short-lived process driven by an (as yet) hypothetical thing called the inflaton field. Regular expansion goes on to the present day and is much more strongly evidenced and better understood. Expansion, in cosmology, is a more general term than inflation and what you are talking about is expansion but not inflation.

However, since we already know that space uniformly inflates or expands, it is obvious that this inflation would prevent us from observing light beyond a certain age -- so therefore we cannot use the maximum age of light that we observe to judge the age of the universe. This is my main point/question that I am trying to understand.

We can't measure the age of light, anyway.

The age of the universe turns out to be one upon the current value of the Hubble "constant". You can estimate that by measuring redshift as a function of distance. There are a variety of more direct measures of ahes of things in the universe that support this - see for example http://www.astro.ucla.edu/~wright/age.html

 

[Bandersnatch]

The age of the universe turns out to be one upon the current value of the Hubble "constant".

That's not strictly true, isn't it? More of a numerical coincidence, thanks to our fortuitous placement in time.

 

[PeterDonis]

The age of the universe turns out to be one upon the current value of the Hubble "constant".

If you just look at the current value of $H$, the relationship between this and the age of the universe is model dependent. To get a handle on which model is the best fit, you need to look at how the value of $H$ has changed over time.

That's not strictly true, isn't it? More of a numerical coincidence, thanks to our fortuitous placement in time.

Sort of. In the far future of our universe, since (according to our current best model) there is a small positive cosmological constant, the value of $H$ will tend towards a constant value, so in the far future there will indeed be no relationship between the age of the universe and the current value of $H$. But until the universe is far into the dark energy-dominated era, there is a relationship between the age of the universe and the current value of $H$; it's just that the relationship is model dependent.

 

[Ibix]

That's not strictly true, isn't it? More of a numerical coincidence, thanks to our fortuitous placement in time.

I don't believe so, although I'm wrong to say it's the age of the universe - it's the age the universe would have if the expansion were linear (i.e. $\ddot{a}=0$), which isn't quite the case. But if it were then the Hubble constant is one upon the age.

Since $\ddot{a}$ isn't zero, it's a little more complex than that and you need to solve the Friedmann equations properly - but it's pretty close anyway.

 

[PeterDonis]

Since $\ddot{a}$ isn't zero, it's a little more complex than that and you need to solve the Friedmann equations properly - but it's pretty close anyway.

The fact that the actual age of the universe happens to be pretty close to $1 / H_0$, where $H_0$ is the current value of the Hubble constant, is because our current best-fit model includes a period of deceleration (radiation and then matter dominated) after the Big Bang (meaning the end of inflation) up to a few billion years ago, followed by acceleration (dark energy dominated) since then. The two periods are roughly equal in time, so the overall result ends up being very close to what a straight linear model would give.

But in the far future, that will no longer be true, because the period of acceleration will get longer and longer as the universe ages, while the period of deceleration is over and the length of time it took is now fixed. So in that sense it is fortuitous that we happen to be living in the era when the actual model happens to closely match a straight linear model.

 

[Ibix]

But in the far future, that will no longer be true, because the period of acceleration will get longer and longer as the universe ages, while the period of deceleration is over and the length of time it took is now fixed. So in that sense it is fortuitous that we happen to be living in the era when the actual model happens to closely match a straight linear model.

Ah - there's a bit more subtlety to this than I'd realized. Thanks.

 

[Bandersnatch]

Sort of. In the far future of our universe, since (according to our current best model) there is a small positive cosmological constant, the value of H will tend towards a constant value, so in the far future there will indeed be no relationship between the age of the universe and the current value of H. But until the universe is far into the dark energy-dominated era, there is a relationship between the age of the universe and the current value of H; it's just that the relationship is model dependent.

Yes, thank you. What I was (very lazily) driving at in my response to Ibix, is I don't think it's ever pedagogically correct to say that the age is 1/H0 when responding to questions about our universe. And most of them are about just that. Not some Milne model or some such, but the concordance model that can be reasonably assumed to approximate what we're living in - because that's what B and I questioners tend to unwittingly assume when they ask about how the universe behaves.

Using 1/H0 to get the approximate age without armouring it in potentially obfuscating caveats creates this perception that it's a relationship that is always true. And then people get confused as they learn more - why is this number different than what they read the age is on Wikipedia? Why is this relation even used if the universe is known to be accelerating? - etc.

We wouldn't be using this approximation if we were discussing this a few dozen billion years in the future, because it'd be very obviously off target. So why do it now?
Haven't we had at least a few posters in the cosmology section confused about this very issue?

Apologies if this sounds at all bellicose. It's just an observation I made after interacting with beginner posters, which is what I mostly do here.

 

[PeterDonis]

What I was (very lazily) driving at in my response to Ibix, is I don't think it's ever pedagogically correct to say that the age is 1/H0 when responding to questions about our universe.

I think we are all on the same page now, given my post #8 and post #9 from @Ibix.

 

[Ibix]

So, to summarise the discussion and make sure I have the right end of the stick, to estimate the age of the universe we first observe that it's homogeneous and isotropic on large scales, and that general relativity is useful. This let's us write down the Friedmann equations and the FLRW metric. That, in turn, let's us write down an expression for the redshift we expect to observe in terms of the distance to the emitting object and $a$, $\dot{a}$, and $\ddot{a}$, which are Friedmann's scale parameter (directly related to the age of the universe) and its derivatives, which depend (through Friedmann's equations) on things like the matter/radiation/dark energy balance in the universe. Then we go out and measure the redshift as a function of distance. We then fit our modeled redshift to the data, and this let's us estimate the scale parameter and hence the age of the universe.

In the case where $\ddot{a}=0$, the equations would simplify and the age of the universe would be exactly one over the Hubble parameter. That is not our universe. In our universe the parameters happen to be such that at the moment the age of the universe is pretty close to $1/H_0$, but that wasn't true in the past and won't be true in the future.

 

[Bandersnatch]

but that wasn't true in the past and won't be true in the future.

One minor correction - the actual age and $1/H_0$ will be getting closer for a while more, and pass a point in time when they are exactly the same (around the 15 Gy mark), before diverging.
Here's a graph of Hubble radius vs time from Jorrie's calculator, showing how increasingly unreliable that approximation will become with age:

 

[Ibix]

around the 15 Gy mark

So I'll be right in about 1.2bn years? Had to happen some time.

 

[PeterDonis]

to estimate the age of the universe we first observe that it's homogeneous and isotropic on large scales, and that general relativity is useful. This let's us write down the Friedmann equations and the FLRW metric.

Yes.

That, in turn, let's us write down an expression for the redshift we expect to observe in terms of the distance to the emitting object and $a$, $\dot{a}$, and $\ddot{a}$, which are Friedmann's scale parameter (directly related to the age of the universe) and its derivatives, which depend (through Friedmann's equations) on things like the matter/radiation/dark energy balance in the universe.

You can write this stuff down in terms of distance in the usual sense, i.e., scale factor $a$, but that's not very helpful because we can't measure that distance directly. What cosmologists actually do is derive model-dependent relationships between redshift and other direct observables, the chief ones being brightness and angular size. They do use the term "distance" in these relationships, but the "distance" they mean is actually brightness converted to distance units ("luminosity distance") or angular size converted to distance units ("angular size distance"). Different models predict different relationships between the three observables, redshift, luminosity, and angular size, so observing the actual relationships tells us which model is the best fit to our actual universe.

Then we go out and measure the redshift as a function of distance.

As a function of luminosity and angular size, which are converted to distance units for convenience. See above.