# Determining The Size and Age of Our Universe

## Main Question or Discussion Point

The Size and Age of Our Universe

If the universe is 14 billion years old, (roughly) then we can only see out in any direction for 14 billion light years. Thus any stars beyond 14 billion light years are invisible to us because their light hasn’t had time to reach us.

If we cannot find an edge within 14 billion light years, then we are farther than 14 billion light years from an edge. Therefore wouldn’t this imply that the universe may be older than we have the ability to discern? And if the universe isn’t a perfect sphere, what then? Do we try detection methods that utilize particles that travel faster than light? Or are we using another method entirely to determine the age and size of the universe?

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marcus
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The Size and Age of Our Universe

If the universe is 14 billion years old, (roughly) then we can only see out in any direction for 14 billion light years. Thus any stars beyond 14 billion light years are invisible to us because their light hasn’t had time to reach us.

If we cannot find an edge within 14 billion light years, then we are farther than 14 billion light years from an edge. Therefore wouldn’t this imply that the universe may be older than we have the ability to discern? And if the universe isn’t a perfect sphere, what then? Do we try detection methods that utilize particles that travel faster than light? Or are we using another method entirely to determine the age and size of the universe?
Current particle horizon is around 46 billion LY. We are currently receiving light (CMB) from matter which is about 45 billion LY from us. This is light we can detect and study and we learn a lot from it.

But we don't say the universe size is 45 or 46 billion LY. The evidence suggests that it is much MUCH bigger. But we can't say how much bigger or even if it is finite. We have to work with what nature gives us and study that and only talk about what we can reasonably hypothesize and test.

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D H
Staff Emeritus
If the universe is 14 billion years old, (roughly) then we can only see out in any direction for 14 billion light years. Thus any stars beyond 14 billion light years are invisible to us because their light hasn’t had time to reach us.
You are ignoring the metric expansion of the universe here.

If we cannot find an edge within 14 billion light years, then we are farther than 14 billion light years from an edge.
You apparently are assuming the big bang was an explosion in space. That's not a good way to look at it.

Current particle horizon is around 46 billion LY. We are currently receiving light (CMB) from matter which is about 45 billion LY from us. This is light we can detect and study and we learn a lot from it.

But we don't say the universe size is 45 or 46 billion LY. The evidence suggests that it is much MUCH bigger. But we can't say how much bigger or even if it is finite. We have to work with what nature gives us and study that and only talk about what we can reasonably hypothesize and test.
How can we observe light from 45 billion light years away if the universe isn't 45 billion years old?

marcus
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DH said it, Scott. You are ignoring the effect of metric expansion. Distances expand. (GR established that geometry is dynamic)
Once light from some matter has traveled a little ways, that distance gets expanded.
Once light has traveled for a year, its distance from its matter-of-origin, the matter that emitted it, is more than a light year.

The CMB is the oldest light we are able to receive with present detectors and study. It was emitted not so long after the start of expansion---maybe around year 370,000---so it has been traveling nearly the whole 13.8 billion years. So when we receive it it is way way more than 13.8 billion LY from its matter of origin.
the matter that emitted it (which we are therefore observing) is now some 45 billion LY from us.

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DH said it, Scott. You are ignoring the effect of metric expansion. Distances expand. (GR established that geometry is dynamic)
Once light from some matter has traveled a little ways, that distance gets expanded.
Once light has traveled for a year, its distance from its matter-of-origin, the matter that emitted it, is more than a light year.

The CMB is the oldest light we are able to receive with present detectors and study. It was emitted not so long after the start of expansion---maybe around year 370,000---so it has been traveling nearly the whole 13.8 billion years. So when we receive it it is way way more than 13.8 billion LY from its matter of origin.
the matter that emitted it (which we are therefore observing) is now some 45 billion LY from us.
Ah, I see, said the blind man. Of course, a billion years from now, if we see light from another billion miles away, then we can assume that the universe is at least another 3+ billion LY to the horizon. Thank you for enlightening me as to what was meant by metric expansion. I knew it didn't have to do with the metric system! ) PS I actually have mastered every course in mathematics that was available in my day, averaged a B+, in fact.

• marcus
marcus
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You are quick off the mark, quick to understand. The amount of matter included in what we call the observable region or observable universe is increasing over time, as more light from farther away comes in. So "observable universe" is not an absolute idea.

I'm a fan of Charles Lineweaver, an Australian cosmologist. He has only written one popularization article I know of, for the Scientific American, co-authored with Davis, a student of his. I have a link to it in my signature in small type at the foot of any post. I don't know if it would be useful to you or not. The Figure 1 link would not necessarily help, it might confuse. I like it because it illustrates that in distance THEN terms the past light cone is pear shaped because stuff was so much closer together back then. Distance then (if you could have paused expansion to give yourself time to measure it) is called "proper distance". The top panel uses proper distance. The bottom two panels use "comoving distance" where you attach to each bit of matter the distance that it is NOW. So in those terms the distance never changes. It's a convenient way of tagging stuff. In those terms the past light cone spreads way out, to like 45 billion LY, or a bit more.

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marcus
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BTW Scott since you had a bunch of math courses (and probably enjoyed them) are you familiar with the symmetrized exponential functions that are traditionally called "hyperbolic functions"?

It turns out the universe makes rather heavy use of a few of them. the names "hyperbolic sine" and "hyperbolic cotangent" can be a barrier to beginners. and I'm poking around now to see if it is possible to introduce them in a relaxed way.

(ex + e-x)/2 is just what you get when you make the exponential function time-symmetric so that it is the same run forwards and backwards (you average the forwards and backwards versions)

And (ex - e-x)/2 is simply the derivative of that. and it is symmetric too in a different sense, flipping left to right and then top to bottom gets you back to the same thing.

That's the hyperbolic sine, conventionally abbreviated "sinh" and it turns out there's a natural time scale built into the expansion process according to which (the present age is 0.8 and) distances, areas, and volumes expand according to powers of sinh(1.5 t).

And on the same time scale it turns out that the Hubble parameter, H(t), the Hubble expansion rate evolves over time according to

$$H(t) = \frac{e^{\frac{3}{2}t} +e^{\frac{3}{2}t} }{e^{\frac{3}{2}t} - e^{\frac{3}{2}t}} = \coth(1.5t)$$

My guess is that you've met these functions in other contexts (without the "3.2" or "1.5" detail). I'm wondering if the idea puts you off that metric expansion, the history of the expansion of distances, has followed and is expected to continue following these functions?

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marcus
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Here's the payoff. It's how the universe's age (time since start of expansion) is calculated based on observations.
I'll skip some steps, and fill in if you are interested and not immediately put off.
If this seems alienating or uninteresting then just ignore it. It's a gamble on my part.
We can observe the present Hubble rate H0 and we can observe how the Hubble rate has been changing recently so can project what its longterm value H will be. The ratio of those two things is 1.201 and tells the expansion age:
By fitting redshift distance data we can estimate the present Hubble rate H0 and the longterm limit that the Hubble rate is tending towards H.

The Age (how long the universe has been expanding) can be calculated just from those two measurements, assuming the spatial-flat standard cosmic model---essentially the Friedmann equation.

Basically you take the ratio H0/H = 1.201

and solve $$x = \frac{1}{3}\ln(\frac{1.201+1}{1.201-1})$$

Then x/H is the Age in whatever units you like to use.
Dividing by H is the same as multiplying by 17.3 billion years. when you calculate
$$x = \frac{1}{3}\ln(\frac{1.201+1}{1.201-1})$$
what you get is 0.8 or more precisely 0.797
that is the age in units of 17.3 billion years. So if you want it expressed in billions of years you multiply
0.8 by 17.3 and get the usual figure of around 13.8

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