A few Universe/Big Bang questions

Factual Questions
1

I have a few hangups on the universe that I can’t seem to get my head around. I tried another forum for this, but did not get a good answer. Maybe I’m not smart enough to grasp it. Or maybe the dopers here will shed more light on the matter.

For reference, here are my “known facts”. If I am wrong about something in these, that would explain a lot!

[ol]
[li]The big bang is always described as a singularity - a point at which everything expanded from.[/li][li]Galaxies do not have enough mass that we can see to keep them together. They are rotating fast enough to tear them apart, yet they remain together.[/li][li]The universe is considered flat. That is if you travel in one direction forever, you will never return to your starting point. This is known to something like 0.4% certainty. This means that space goes on forever.[/li][/ol]

Based on these three facts, here are my three deductions that are apparently wrong :confused:. Why are they wrong and where did my logic fail?
[ol]
[li]How do we really know the age of the universe? We see everything expanding and we calculate that expansion rate back to time 0. And we get 13.7 billion years. But inflation came first with a massive speed boost. Then it apparently slowed down via gravity. Then it apparently started speeding up again to which we created a name of dark energy to explain. So the rate of expansion is absolutely not constant. We’ve been monitoring this for only a few decades. So how do we get to the 13.7 billion year age? No mathematical curve would fit all the unknowns in the expansion rate. Sure, if it was constant, then I’d be on board.[/li][li]The matter in the universe cannot be infinite. No amount of speed can ever take that original singularity and bring it to infinite size. If it was as small as a pin head at one point, it’s still a physically measured size today. Yet it seems the general consensus in the community is that matter is infinite. How? I usually get a horrible analogy here. I’m told to envision an expanding balloon. And an ant walking on it. The balloon is expanding everywhere at once, and there’s no center. Wrong… There’s a center inside the balloon! Furthermore, in this example, the ant could walk around the balloon and get back to where it started. This is not the flat universe I’m told we live in.[/li][li]The universe has a center. Not that we can see of course. We are the center of our own observable universe. Let’s say for example that the original singularity shot out a sphere of matter that is still expanding. It’s now 1 trillion light years across. There’s a center darn it! It’s in the middle of the sphere. The original point. Now we may be anywhere inside the sphere. We can’t see the center nor ever find it. But, if the universe is finite and not infinite, then there must be a center. If the universe’s matter is truly infinite and goes on forever, then there’s no center. But in that case, the matter was infinitely everywhere at the time of the big bang and there could have been no singularity.[/li][li]Dark matter. We see that galaxies should fly apart. So we postulate that there must be more matter than we are seeing. Makes sense so far. Then we label it as matter that never interacts with other matter so we can’t detect it. Huh? This explanation is about as creative as “God made it that way” when a kid asks why the sky is blue. It blindly comes up with any answer to fill a question. I have no problem with a hypothesis and testing. But it seems every physicist/astronomer always has the attitude of “we know it’s there”. What if there are trillions of planets floating around that we can’t see because they are not around a star? What if there are 500 billion black holes in our galaxy from stars that burned out long ago? That’s ‘dark matter’ too. Wouldn’t an explanation like that solve the galaxy issue without creating special exotic answers?[/li][/ol]

Please note that I’m not trying to be argumentative. I’m sure there are valid answers here.

2
  1. Dark Matter. I think you are getting Dark Matter and Dark Energy mixed up. Dark matter explains why the outer stars within a galaxy rotate faster than theory predicted. Other observations such as gravitational lensing add weight to the idea that this extra mass exists.

Dark Energy is posited to explain why the expansion of the universe (i.e. galaxies flying apart) seems to be speeding up rather than slowing down as expected. You would expect gravity from all the mass in the universe to slow expansion so something must be giving expansion an extra oomph to push galaxies apart. We don’t know what that extra oomph is so it is “dark”.

3

I’ll address the second question first. The expansion of the Universe does not have a speed. Particular points within the Universe are receding from each other at some speed, but that speed depends on how far apart the points are. This is expressed in terms of the Hubble “Constant” (in quotes because it changes with time), which is about 70 kilometers per second per megaparsec. That is to say, two points a megaparsec apart are currently getting further apart at a rate of 70 km/s, and two points two megaparsecs apart are currently getting further apart at a rate of 140 km/s, and so on.

If the Universe is infinite (which isn’t actually known, incidentally, though the simplest models consistent with the evidence say it is), then it’s always been infinite, at any time after t=0. Right exactly at t=0… well, we can’t say anything about anything. Divide by cucumber error.

Now then, on to question 1: If you take that figure of 70 km/s/MPc, and play with the units, you’ll realize that it’s actually just an inverse time. Take the reciprocal, and there’s your first estimate for the age of the Universe: If we have that Hubble constant right now, and there has been no acceleration over the entire history of the Universe, then that’s the age of the Universe. Now, of course, that’s not quite right, since we do have some acceleration, but it’s easy enough to include that in the models, too, and so get a better acceleration. There was an extremely large acceleration during inflation, which we don’t know much about, but since inflation lasted for a very short amount of time, it doesn’t actually make much difference to the calculation of the age (if you prefer, you can think of the age figure as being the time since the end of inflation, rather than being the total time since The Beginning).

Third question:

Your first sentence is just fine. For your second sentence, though, again, it’s infinite at any time after The Beginning, but we can’t say what it is right exactly at The Beginning. It might be easier to think about in terms of density, instead of absolute size: The closer you get to The Beginning, the higher the density was, with no upper limit. As you approach The Beginning, the density approaches infinity. It’s the infinite density that’s the singularity.

For finite universes, there still probably isn’t a center. Have you ever played a video game where the edges of the map are identified? If you go off the west edge of the map, you’re on the east edge, and if you go off the bottom, you’re on the top. The way the map is presented on a page of the manual, it looks like it has edges an a center, but you can draw the edges anywhere else and come up with a different center.

Fourth question: It’s not that dark matter doesn’t interact with “ordinary” matter at all; it’s that it doesn’t interact electromagnetically. It certainly interacts gravitationally, and it might or might not interact via the strong and weak nuclear forces, which are too short-ranged to be relevant at astronomical scales. This shouldn’t be all that surprising, as we already know of some examples of particles that behave this way, such as neutrinos. There have been some other attempts to explain the evidence without invoking dark matter, but there are many different independent lines of evidence, all of which are consistent with dark matter, and none of the alternate explanations accounts for more than one or two.

As for the nature of dark matter, you mention planetlike objects in deep space, or black holes. Those certainly exist, and certainly account for at least part of the dark matter. You and I are made of dark matter. But all of that is what’s called baryonic matter (well, the black holes aren’t, but they started out as baryonic). The problem is, we can say just how much baryonic matter there should be in the Universe, and it’s not enough. When people refer to “dark matter”, they usually mean “non-baryonic dark matter”, the mysterious stuff that makes up the rest and which we don’t know what it is.

How do we know how much baryonic matter there is? Baryonic matter is so called because most of its mass is due to protons and neutrons, which are baryons. The nuclei of elements are made up entirely of baryons. Some nuclei, such as all of the isotopes of hydrogen, lithium, and beryllium, were formed entirely in the early Universe, when baryons were first starting to bump together. How many of each isotope we ended up with depends on how abundant the baryons were back then: If there were a lot of them, then bigger nuclei would be common, and if there were few, then big nuclei would be relatively rare. So the relative abundances we actually have serve to tell us how abundant baryons were back then, and since there’s nothing that changes the number of baryons (aside from turning into black holes, but we already said we’re counting those too), that’s how many we still have.

4

  1. It’s actually fairly easy to hit the rewind button on the Universe to see what it was like in the past as on a large scale in some ways it’s very simple and governed by only a small number of parameters. NB a constant expansion rate is actually impossible in general relativity (or at the very least needs a very fine-tuned field to be introduced). That said you get to a certain point in the very distant and the physics becomes much less certain, however this period must be very close to the big bang and so doesn’t add a huge amount of uncertainty to the Universe’s age.

  2. A singularity in general relativity is when a certain input into the equations fail to meet some set of conditions. An infinite Universe is infinite throughout its history.

  3. Obviously if the Universe is infinite then your objection is null, but even finite cosmological models don’t have centres. The sphere might have a centre in when embedded in 3-D space, but there is no centre on the surface itself.

  4. The simple answer is that whilst black holes and planets make up a percentage of the ‘dark mass’, the predictions of models where these type of objects made up the bulk of dark matter differ significantly from what is observed. A simple process of elimination tells us what dark matter isn’t, but it can’t tell us what it is as our models tell us it is certainly a type of matter that is not very amenable to observations beyond its gravitational influence.

5

There is a search going on for dark matter right now nearly a mile underground in South Dakota. Nothing found so far, but this particular experiment has produced the most precise null result yet! Just search for “lux dark matter”

LUX (Large Underground Xenon experiment) first results.

6

Perhaps your intuition can sharpen a bit by imagining a 2-dimensional world. It could be the surface of a sphere, which is not flat, but, in any case, has no center. But to detect the non-flatness, you would have to measure the sum of the angles of a triangle and find they total more than 180. But the excess over 180 is determined by the ratio of the area of the triangle to the area of the sphere. For example, a triangle with three right angles has an area of 1/8 the area of the sphere, while its complement has three angles of 270 deg has an area of 7/8 of the sphere. The “angle excess” (the amount over 180) is 90 in the first case, but 630–7 times as large–in the second. Now imagine how large an angle we can measure. I think the longest baseline we can get is the diameter of the earth’s orbit and that will give triangles a minute fraction of the size of the universe. (Okay, I have slipped from 2 dimensions to 3, but the principles remain the same.)

Then there are other shapes, even finite ones that flat geometries. In 2 dimensions, a torus can be given a flat geometry. While the usual geometry on a torus is not flat, there is one that is. Imagine a flat square with its usual flat geometry. Now modify it so that the distance between a point on the left edge to the corresponding point on the right is 0. Do the same for the top and bottom edges. The figure is now a torus geometrically, but the geometry is flat. You have to be careful since the distance between, say, a point near the left edge and one near the right edge may be less than it used to be because there is no a segment between them that crosses thos edges. Of course, those edges have disappeared and the torus is completely homogeneous.

There is also a 3 dimensional torus gotten by starting with a cube and making the distance between corresponding points on opposite faces to be 0. And a 4 dimensional torus and…

7

I think much of your confusion lies in thinking that the matter in the universe all originated from a single point in space and the big bang was like an exploding black hole, when actually it’s space itself that’s expanding. Various objects in space aren’t moving very quickly through space; it’s just that two distant points of space are moving apart quickly. You can somewhat think of it as though the Earth was growing in size. Two cities that started out, say, 1,000 miles apart might eventually be 2,000 miles apart, but neither of them actually moved anywhere.

8

Well, it is actually like an exploding black hole, but that’s not a very useful description, since most people don’t really have a clue what an exploding black hole is like.

9

It’s my understanding that early in the universe, matter filled all of space as it does today (but was more dense) whereas in a black hole, matter is contained within one point of space. Is this not the case?

10

In a black hole in equilibrium, yes (or at least, that’s what the best theories we have say, though there’s necessarily some extrapolation involved there). And black holes reach equilibrium quite quickly, relative to their size. But not quite instantaneously, and for a sufficiently-large black hole, the difference can be significant.

You remember the speculation that the Universe might eventually collapse into a Big Crunch? If that happens, then the Universe isn’t only like a black hole, it is a black hole. The Big Crunch is the center. Not everything has reached the center yet, but it will, inevitably. Now, our best evidence currently suggests that it won’t collapse into a Big Crunch… but it’s still in many ways similar to a universe that would, so it’s fair to say that it’s like a black hole.

11

The definition of a black hole is incredibly tricky, but I’d disagree with the idea of a closed FLRW Universe as a black hole as it doesn’t really fit with the notion of what a black hole is. The notion of a black hole as a region of space where nothing can escape is much more easy to pin down than the formal definition.

12

I have a related question re: Age of the Universe and the Cosmic Microwave Background (CMB).

In cosmology books, there is often a historical review describing numerous (usually upward) revisions of the estimated age of the universe, based on revisions of Hubble’s constant. This was sometimes due to better measures and sometimes due to re-evaluation of “standard candles”.

After WMAP sent back it’s CMB map, we settled on 14.7 billion years.

Is this a different methodology? (Is it easy to explain? This is my main question.) Is it better? (By that I mean does it rely on less assumptions or extrapolations?) Are future CMB missions likely to change that number (by more than refining decimal places)?

13

When calculating the age of the Universe there’s also a dependence on the model used, so improved models lead to improved estimates of the age of the Universe.

The age estimate produced by WMAP was based on the Lambda-CDM model, the ‘standard model’ of modern cosmology. The older estimates were based on not just less accurate data, but also on more models that were cruder/not as good fits to (subsequent) observation. Below is a link to the six parameters of the Lambda-CDM model measured by WMAP which were used to calculate the age of the Universe:
http://en.wikipedia.org/wiki/Lambda-CDM_model#Parameters

NB the estimated age was 13.75 Byrs

14

In answer to your 2nd question, assuming the WMAP data isn’t flawed, further measurement will only refine the estimate based on the Lambda-CDM model, but it’s entirely possible that an improved model could change the accepted best estimate more radically.

15

What’s a billion years between friends? :slight_smile:

16

The MAP data is incredibly better than anything that came before. Before MAP, any cosmologist would tell you figures like the Universe’s age only to within a factor of two or so. The joke was that if you asked a cosmologist for his phone number, he’d tell you “It’s of order 10^7”. After MAP, it became possible to answer questions like that to within about 1%.

17

So the WMAP data gets plugged into lamda-cdm to calculate Hubble’s constant (which is more precise than values measured by redshift?

18

As an aside: the Planck mission has surpassed WMAP as the bleeding-edge precision CMB experiment.

You can plug the CMB data alone (either Planck or the older WMAP data) into the model to determine the best model parameters and their uncertainties, but generally the CMB data is combined with supernova data, large scale structure measurements, gravitational lensing data, and polarization data from other instruments to achieve the best constraints. The CMB data alone does a pretty impressive job on its own, but each of these other sources of information has different connections to the model parameters, so the combination helps pin things down.

Note that all these data sources vary greatly in nature, and the Lambda-CDM model could have simply failed to describe all of them simultaneously. The fact that it succeeds (with only the usual nitpicks here and there) says a lot about the model.

For the age of the universe in particular, Planck data alone yields the answer to 0.42% precision, and adding in other cosmological data reduces that to 0.27%.

19

The scale factor a(t) is the function that tells you how the distance between comoving objects (such as galaxies, galactic clusters or any object with suitably negligible peculiar velocity) changes with (cosmological) time. For convenience at the present time t[sub]0[/sub], a(t[sub]0[/sub]) = 1. At the big bang a(t) = 0, so to work out the age of the Universe you need enough information about the function a(t) to calculate the value of t such that a(t[sub]0[/sub]-t) = 0.

The Hubble constant is a’(t[sub]0[/sub])/a(t[sub]0[/sub]), which is a quantity you can calculate if you have enough information to work out the age of the Universe, but in itself doesn’t tell you enough about a(t) to calculate the age of the Universe.

20

True, but that’s mostly just an incremental improvement: Planck is doing basically the same thing that MAP did, just doing it a bit better (well, and also getting polarization information, which is nice). It’s not revolutionary in the same way that MAP was.

Of course, I suppose you could also say that MAP was just an incremental improvement to COBE, except that that was a large enough increment that it enabled us to do entirely new sorts of scientific analyses.