Does the Cosmological Constant Exist?

[newton1]

is that cosmological constant exist??

 

[mathman]

The cosmological constant appears in the basic equation of general relativity. The major question is its value. Current theory, based on the observed acceleration in the expansion of the universe, says that it is small, but not zero. However (and this tends to be so for any new ideas in science) it is still an open question. There are other theories to explain the observed acceleration, although the non-zero cosmo. constant seems to be most in favor.

 

[newton1]

why Einstein said this is his greatest mistake?

 

[Janus]

The science of the Lamda

Originally posted by Newton1
why Einstein said this is his greatest mistake?

At the time That Einstein first formulated his field equations of GR, the general consensus was that the universe was static. Gravity, however would tend to cause a static universe to collapse in on itself. Einstein added the cosmological constant(lambda) as a factor to prevent this.

It was later shown that unless the lamba was precisely the correct value, it would lead to run away expansion or contraction of the universe.

Then Hubble discovered the recesion of the Galaxies. If the universe was flying apart from some intial impetus, its own momentum was what was keeping it from collapsing (at least for now and the near future). This made the lambda unnecessary.

This discovery of the expansion of the universe made Einstein feel that he had added an un-needed term to his equations, thus he concidered it a mistake.

It wasn't until recent evidence that the universe's expansion is accelerating was uncovered that the lambda has been been brought back into the lime-light.(This is precisely the type of runaway expansion predicted earlier.)

 

[Nacho]

Janus,

But is it really runaway expansion now, or do the observations just show that expansion is increasing at a low rate? If it just means expansion increasing at a low rate, that would suggest to me that it's something that had started recently, in terms of cosmic time.

That would suggest a coincidence that we are here to view it just now, unless the rate had been increasing from near the beginning. I think that could be tested, assuming Inflation occurred, and that the distribution of matter in the Universe today is an imprint of a quantum fluctuation grown to hugh porportions VIA Inflation. The amount that Inflation would have blown it up, plus the amount that "flat" expansion would have blown it up, taken away from the distance between galaxies today (statistically, the Universe as a whole), would put an upper limit on how fast the expansion could have increased.

 

[Janus]

Originally posted by Nacho
Janus,

But is it really runaway expansion now, or do the observations just show that expansion is increasing at a low rate? If it just means expansion increasing at a low rate, that would suggest to me that it's something that had started recently, in terms of cosmic time.

Basically, the observations show that the universe's rate of expansion has increased over time for as far back as we can see. (Remember, the further we look away, the further back in time we are looking. ) By comparing the distances of galaxies with their red-shift, you can plot the rate of expansion over time.

The original investigators were actually expecting a deceleration in the rate over time, caused by the mutual gravitational attraction of the universe. They were trying to determine whether or not there was enough matter in the universe to eventually stop and reverse its expansion. They found the opposite.

 

[marcus]

here's a page on the cosmological constant from Ned Wright's site

http://www.astro.ucla.edu/~wright/cosmo_constant.html

It says a lot of the same things as Janus and it also summarizes some arguments AGAINST the cosmo constant (which should interest Nacho)

and it also discusses, as Janus did, the reason Einstein regretted having introduced the Lambda into his equation and called it his "greatest blunder"-----so that may interest Newton, since he asked about that.

On this Ned page one of the figures the thing that I am seeing more and more of which is a plot of the a(t) curve over time----
the plot of the scale-factor from around one picosecond up to the present, and projected on into the future sometimes too.

This curve seems to have the best fit to the supernova data and the CMB data if a certain value of Lambda is chosen and held constant throughout. It leads to an inflection point (as you can see in the figure) at maybe a billion or two years ago.
Expansion slowing until then and then roughly steady and then gradually beginning to accelerate. This is what one expects from having a constant Lambda because at first matter and radiation dominate the energy density and as they thin out the Lambda or vacuum contribution becomes more significant and has a more visible effect.

The best scale-factor curve----showing how a(t) grows over time---at least that I have seen, is in Lineweaver---Figure 14 on page 30

http://arxiv.org/astro-ph/0305179

This is also the most recent. It shows the same inflection point behavior as the NedW figure. Lineweaver's article is also at the CalTech "Level 5" site, so that would be a quick way to get to his Figure 14 in HTML without having to download a PDF file. I will give the Cal Tech link later when I find it.

This scale-factor curve is what has to fit the data, in the last analysis, so it is worth checking out and seeing how various assumptions influence the shape of the curve.

edit: for Lineweaver's Figure 14 at the Cal Tech site scroll 2/3 of the way down this page:
http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Lineweaver7_7.html

also if you want a high-resolution picture you click on that one and you get this JPG that fills the screen:

http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg

 

[Nacho]

marcus,

Thanks for the links. Most of them are WAY over my head .. I took a quick look at them, and printed them out for study tonight.

Janus,

I didn't make myself clear. I (kinda) already understood the observations they made and how they came to explain it as the rate of expansion of the Universe is increasing. What I was trying to get at is this (hope this is a better job of asking the question):

I find it hard to believe an increase in the rate of expansion is starting just now, in this era of the Universe. That's a centrist view, so I can't believe that (not that anybody here has that view either though). I'm more inclined to believe if there is now an increase in the rate of expansion, that it has been around since somewhere close to the BB.

If so, I'm under the impression that rate should have been increasing for billions of years, and would diverge from the number it started at .. sort of like a geometric progression. So that the effective rate the Universe is expanding now should be very-very hugh, not what the Hubble Constant shows. Also, it seems to me our observations should show the Universe as a whole would not follow a Hubble Constant as a line, that is a graph of distance vs redshift should show a curve, not a straight line. That is because the light we are getting from galaxies billions of light years ago would have been emitted when the effective rate of expansion was lower. The light we get from closer galaxies was emitted when the effective expansion rate was higher. And charting redshift to distance should show that curve.

Assuming what I said above is true (doubtful ;) ), that's how I came up with the idea of using a measure/upper limit on how much this increase in the rate could be, and compare that to a limit brought on by way of the super-nova observations, looking for discrepancies.
But, in reading one of those links marcus left, the amount of expansion caused by Inflation cannot be tracked good enough to yield any results for comparison.

Maybe I'm asking for observations, the accuracy needed is not available. Or I'm totally lost??

 

[Janus]

Originally posted by Nacho
marcus,

Thanks for the links. Most of them are WAY over my head .. I took a quick look at them, and printed them out for study tonight.

Janus,




I'm more inclined to believe if there is now an increase in the rate of expansion, that it has been around since somewhere close to the BB.

That's basically what the observations show.

If so, I'm under the impression that rate should have been increasing for billions of years, and would diverge from the number it started at .. sort of like a geometric progression. So that the effective rate the Universe is expanding now should be very-very hugh, not what the Hubble Constant shows.

That would entirely depend on how large the rate of expansion is. If it is very very small, The present rate of expansion is what it has built up to.

Also, it seems to me our observations should show the Universe as a whole would not follow a Hubble Constant as a line, that is a graph of distance vs redshift should show a curve, not a straight line. That is because the light we are getting from galaxies billions of light years ago would have been emitted when the effective rate of expansion was lower. The light we get from closer galaxies was emitted when the effective expansion rate was higher. And charting redshift to distance should show that curve.

Again, that's exactly what the observations showed. No one really believed that the Universal expansion followed the Hubble constant exactly, only that it followed it closely enough for it to be a good "rule of thumb". (The curve is small enough that it seems nearly flat.)

The investigators were looking for just such a curve in actual measurement vs. ideal Hubble constant. They just found that the curve went in the other way than they expected.

 

[marcus]

Originally posted by Janus
Basically, the observations show that the universe's rate of expansion has increased over time for as far back as we can see. ...

that is not my understanding of what the observations show.
It sounds like it would mean the scale-factor curve has increasing slope from the very start. On the contrary, the plots of this curve that I see in Lineweaver and in Ned Davis tutorial have decreasing slope, then an inflection, and then increasing slope.

It is actually hard to tell where the inflection point comes, maybe sometime in the past billion (or two billion) years.

If you have an article by some cosmologist that plots it differently, say with increasing slope all along from the start, it would be really interesting to see and compare with these other sources!
Please post some links!

In case you want to take a look, I posted links to the CalTech Lineweaver site and to Ned Wright's picture earlier in this thread, but I expect you know them anyway.

 

[marcus]

Originally posted by Nacho

Janus,

I'm more inclined to believe if there is now an increase in the rate of expansion, that it has been around since somewhere close to the BB.

----------------------------------------

Originally posted by Janus

That's basically what the observations show.

this has me quite puzzled
everything I've read has the expansion rate decreasing for a long period of time (on the order of 10 billion years) because of
matter dominance

and only after that long period of decelerating expansion is the matter thinned-out enough so that the accelerating effect of the cosmological constant is seen

where is this other view of things written up?

 

[Janus]

Originally posted by marcus
this has me quite puzzled
everything I've read has the expansion rate decreasing for a long period of time (on the order of 10 billion years) because of
matter dominance

and only after that long period of decelerating expansion is the matter thinned-out enough so that the accelerating effect of the cosmological constant is seen

where is this other view of things written up?

Your quite right. I wasn't very clear. What I meant was that the expansionary "effect" was always there. Of course, it would have been over-shadowed by the decelerating effect caused by mutual gravitation during the early stages, just like you said.

Put it down to trying to rush off a post too quickly, too late at night.

 

[marcus]

Originally posted by Janus
Put it down to trying to rush off a post too quickly, too late at night.

For my part I find it easy to write unclearly at any time of day. It happens naturally all the time.

I am wondering how to describe that nice shape of curve
that the cosmologists plot for the "size" (or more precisely the scale-factor) of the universe.

It is related to an S curve, but slanted so that it is always rising.

I mean how do you describe it to a non-mathical person so that he/she immediately gets it.

It starts out convex and then inflects and becomes concave...is there something familiar to compare this to.

 

[marcus]

...is there something familiar to compare this to.

Yes, I had another look at
http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg

the solid dark line is the standard curve assuming (0.27, 0.73) for data
and it looks like the silhouette of a woman's front down to the nipple, which is at time zero. Do you agree?

 

[Nacho]

I understand the concept now .. the graph tells all. It was also included in the Lineweaver ph.0305179 article you linked, marcus.

It kinda conjures up the thought to me that Inflation is viewed backwards; that it is the normal operation of the Universe, and was stopped for a period of time by something after the BB, but is picking up steam again ...

Wonder if these observations will hold.

 

[marcus]

Originally posted by Nacho
I understand the concept now .. the graph tells all. It was also included in the Lineweaver ph.0305179 article you linked, marcus.

It kinda conjures up the thought to me that Inflation is viewed backwards; that it is the normal operation of the Universe, and was stopped for a period of time by something after the BB, but is picking up steam again ...

Wonder if these observations will hold.

In the most general definition I've seen (probably you've seen it defined this way too) an inflationary epoch is simply one of accelerating expansion.

That is what inflation is------expansion that accelerates.

Then there is that PARTICULAR split second case of accelerated expansion that is imagined to have occurred sometime in the first picosecond. But that is just a special case of the general thing.

I am just repeating what you said with more words.

The celebrated split second inflation that is postulated to have happened is driven by a very similar mechanism as todays (much much slower) inflation-----namely a constant energy density.

In the famous Guth/Linde etc case the energy density is called a "scalar field". Or sometimes the "scalar field" is called the "inflaton".
But it is very much the same sort of machine as Lambda----just a constant energy per unit volume-----like the evenly distributed vacuum energy.

The whole point of a constant or even nearly constant vacuum energy is that it creates a negative pressure which the Einstein equations (paradoxically almost) say is expansive.
Einstein knew that a constant vacuum energy would be expansive back in 1916 when he snuck the Lambda into the equation (in an attempt to keep his static universe from beginning to fall together, he fine-tuned Lambda to be the right size to balance the tendency to collapse---obvious fudging)

The equations are simple but the thing itself is strange.

What you say about accelerated expansion being somehow the normal state of things is very reasonable, given what is now known---but nature always seems to have surprises in store, sorry if that seems a cliche but it has been that way in cosmology for a while hasnt it?