[Martin]

Before posting on cosmo topics consider getting squared away on the conventional standard version. There are several great tutorials, for which I'll post link. And the standard model universe is embodied in some online calculators---playing around with them gives you some hands-on experience with redshifts, recession speeds, distances and so forth.

Here's the authoritative up-to-date Einstein-Online tutorial on cosmology, written in understandable non-mathy language.
http://www.einstein-...logy/index.html

It is the cosmology part of a broad outreach site maintained by the Albert Enstein Institute, a worldclass science outfit in Germany. Here is the main Einstein-Online index in case you want to look at their other stuff:
http://www.einstein-...ghts/index.html

An article that has been recommended a lot by many different SFN posters is this one by Lineweaver and Davis
www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
It was published March 2005 by SciAm---the Einstein-Online material is more recent and more comprehensive
but Lineweaver article is still useful. It is used in a Princeton astro course, so an alternative copy is
available online at princeton.edu if this Aussie National University link should ever not work.

It makes understanding cosmology much easier if you train your imagination to think visually about changing distances.
The Hubble law is a pattern of increasing distances between stationary objects (galaxies are taken as approximately
stationary and the distances between widely separated ones increase at a regular percentage rate.) A good way to
train your imagination to visualize changing distances is to use Ned Wright's computer animation balloon visuals.
If you ever need the links, they are the first two google hits with "wright balloon model". I will give the links but all Ned Wright's stuff
on cosmology is really easy to google, so I hardly need to. I'd advise anyone new to cosmology to spend a few minutes
with each model. Galaxy stationary means it stays at the same latitude and longitude on the balloon. The wriggling photons
of light are not stationary, they gradually creep across the empty space between galaxies. If you have this visual thing well
assimilated, a lot of what you encounter in cosmology won't seem surprising or incredible.

www.astro.ucla.edu/~wright/Balloon.html
www.astro.ucla.edu/~wright/Balloon2.html

Before you post your own personal cosmology ideas I would suggest you take the time to understand the standard version. This may mean that you start off at this forum asking questions rather than immediately expressing your own views. The point is to have a secure understanding of what you deviate from, as a kind of home base. It makes communication more efficient if there is a shared understanding of the mainstream picture.

One thing that everybody should have done, who wants to talk cosmology, is play around with the online cosmo calculators. It's an easy way to get to know standard cosmology because that is what is built in to the calculators.
The Ned Wright version is the google hit you get with "wright calculator".
I'll give the link here as well, even though it is so easy to google:
http://www.astro.ucl.../CosmoCalc.html

Personally I like a different one, Morgan's cosmos calculator, so I'll give the link to that too:
http://www.uni.edu/m...ogy/cosmos.html
The labels on this one are less technical and some people find it easier to immediately pick up and use---user friendly. The only downside is that at the beginning of every session you have to type in three numbers: .27, .73, and 71. These are standard cosmology parameters. Ned Wright puts them in for you as default settings, but Morgan makes you type them in. Those already experienced with this will recognize these numbers as the matter fraction, the dark energy fraction, and the Hubble rate.

That's all we need for starters I think. What I plan to do is discuss some of these things I've mentioned in the next few posts, and encourage everybody who wants to post in cosmo forum to get familiar with these basics.

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The desired header on the new post is Cosmo Bronco--a crash course in basics, or for some a refresher
Ideally for the sake of reader-friendliness, the following should be a separate post: the #2 post of the thread.
Since I can't make it a separate post, please think of it as separate.
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There are different ways to approach this material, to suit various people's needs. There's this crash course, for people who are up for it. I'll describe that way in, and then we can talk about more gradual approaches.

The crash course goes like this. We assume you have visited the Einstein-Online cosmology site and read some stuff there that interested you.

We assume you know the FRW metric, the distance function, that tells timevarying distances between stationary objects, and the scalefactor a(t) that plugs into the metric and as it increases causes spatial distances to increase.

We assume you know that the redshift is (one less than) the factor by which distances have increased while the light was in transit. It is a convention to deduct one, so that to get the ratio of distance now to distance then you have to add one to z.

z+1 = a(now)/a(then) the factor that distances are bigger by, now as we receive the light versus then when the light was emitted.

And we assume that you know the CMB redshift is about 1090. that is a conventional figure for it. So you go to wright's calculator and plug in 1090
http://www.astro.ucl.../CosmoCalc.html

Now your job, if you choose to be a volunteer member of the crash course, is to interpret what you see in the calculator windows, when you put in z=1090 (and click the button to make it calculate). If you can interpret even half of what the calculator gives you, then you pass the course :D

Any takers?

PS: You might also try z = 1090 in Morgan's www.uni.edu/morgans/ajjar/Cosmology/cosmos.html remembering that in that case you have to
type in the numbers .27, .73, 71 that Wright's gives you automatically. Morgan rounds off its answers and uses more self-explanatory labels, so it is less precise and at the same time more accessible.

If you don't have the URL handy, an easy way to get to Morgan's is simply to google "cosmos calculator"
Be sure to include the final S on "cosmos".

This post has been edited by Martin: 19 October 2008 - 01:32 PM
Reason for edit: multiple post merged

[interstellar]

Hello I run a website for beginning astronomers, I hope they can get some use out of it. Thanks and have a great day.

This post has been edited by YT2095: 21 October 2008 - 10:54 AM
Reason for edit: offsite linking

[Martin]

I want to add a couple of things to the cosmo basics thread:
A. what to learn from the balloon picture of expanding distances.
B. Lineweaver's Figure 1 from his 2003 paper---how the horizon has evolved.

A. Balloon picture
www.astro.ucla.edu/~wright/Balloon.html
www.astro.ucla.edu/~wright/Balloon2.html
Probably over half of us SFN members have at one time or another advised someone else to imagine an expanding balloon as a way of understanding how space geometry changes with time. How distances between stationary points increase.

Like any analogy, not to overinterpret or take too far. Space is not a material as far as we know, not like rubber. The simplest idea of space is it is just a bunch of distances. The balloon with dots stuck on for galaxies is a 2D analog of 3D space. It teaches about the STANDARD no-frills version of cosmology.

What can one learn by studying the balloon image.

1. no edge, no boundary, matter distributed uniformly throughout space (for the infinite version just picture a *really* big balloon ;) but it's OK to learn on the finite version)

2. all existence is on the balloon surface, no other dimensions, no other directions you can look or point in.

3. idea of being stationary with respect to the CMB, the matter which radiated the CMB. the CMB is symmetric around you with no doppler hot or cold directions, the expansion is symmetric around you, you are at rest wrt the universal rest frame. this corresponds to staying at the same latitude and longitude on the balloon. that is what the galaxies do. the photons of light move among the galaxies, they are not at rest. (watch Wright's balloon animation and get this image in mind)

4. all largescale distances between stationary points (outside stable structures like galaxies, in which stuff is gravitationally bound together) are increasing by a certain percentage per minute---or per million years. that's Hubble law. Currently 1/140 of a percent every million years but the rate changes. Distances between stationary points increase faster the larger the distance is. Look at the balloon animation.

5. Locally nothing MOVES faster than the photons of light. In spite of the fact that the individual galaxies get farther apart they are not moving in the way the photons are. The photons wriggle past them always at the same speed of 1 inch per minute or whatever.

The balloon animation can help you visualize the pattern of changing distances, and how the matter which radiated the CMB which we are now receiving is today 46 billion lightyears from us.


B. Lineweaver graph of a shifting cosmo horizon (there was a question about this thx to BabyAstronaut, so I've included a brief explanation.)

http://arxiv.org/abs/astro-ph/0305179
Download the PDF and look at page 6, Figure 1. The top section is drawn in real physical distance (instantaneous segmented radar distance between points stationary wrt CMB) The other two sections are special-purpose re-mappings. Let's focus on the top section.

Notice that past lightcones are teardrop shape. Notice how the Hubble radius is increasing and asymptotically meets the cosmological event horizon. If we use typical standard model parameters the limiting value for both is 16 billion lightyears.

That comes from the Friedmann eqn. The Hubble radius at time t is c/H(t).
H(t) --> sqrt(0.73)H(now) as t --> infty
Hubble radius --> 13.77/sqrt(0.73) billion lightyears = 16 billion lightyears.

If anyone is interested I'll go into more detail, if not, won't waste time.

Point here is that you can learn a lot of basic cosmology just by studying the balloon analogy and Lineweaver's 2003 Figure 1.

Ask questions if you want to pursue this.

http://www.mso.anu.edu.au/~charley/

This post has been edited by Martin: 30 October 2008 - 10:14 PM

[Martin]

It's advisable not to refer to the BB as the "origin" of the universe because scientifically speaking the classic BB model describes the early universe back to within a few planck times of where it fails, but does not describe anything that could be called an initial state or a beginning.

Talking as if the model describes a precise beginning (at some putative t=0) is incorrect, and it can easily confuse noobs---and lead to sterile argument.

Math models in physics commonly have a domain of applicability---the only give sensible answers well within certain limits. If you push them too close to their limits you can't trust the numbers the model gives you. Classic GR and the classic cosmology model is not reliable once you get within a few planck times of t=0. Amd at t=0 it simply doesn't compute (that is in fact how the time-marker t=0 is defined.)

So the classic BB model is acknowledged to be incomplete. It has no origin or initial state. Current research is aimed at extending the BB model to the t=0 point and beyond.

The new BB models also do not describe the "origin" of the universe. They simply go back further in time. Typically what is found is space time and matter obeying the same laws.

In some, there is no scientific reason to postulate a "beginning" of the universe. It is incorrect to talk about an origin whether in the classic context of the old BB model or in the context of the new BB models. None of the models involve a beginning or an initial state. So the word "origin" quite possibly is without meaning (applied to the universe).

Of course it can be meaningful to talk about the start of expansion. That is a well-defined event at least in some models. But in those models the start of expansion is not the beginning of the universe, because they describe prior process leading up to the start of expansion.

So it is legitimate to talk about the beginnings of various phases occurring in some stated BB model.

But when talking about BB theory it's not so good to be referring to the "origin of the universe".

[Martin]

The most recent values of cosmo model parameters are here
http://arxiv.org/abs/0803.0547
Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation

E. Komatsu, J. Dunkley, M. R. Nolta, C. L. Bennett, B. Gold, G. Hinshaw, N. Jarosik, D. Larson, M. Limon, L. Page, D. N. Spergel, M. Halpern, R. S. Hill, A. Kogut, S. S. Meyer, G. S. Tucker, J. L. Weiland, E. Wollack, E. L. Wright
(last revised 17 Oct 2008)

For instance this gives 95% confidence intervals for the curvature parameter Omega_k. See table 2 on page 4*.

These are based either on WMAP data alone or WMAP (microwave background) taken together with SNe (supernovae) and BAO (galaxy counts at various distances---redshift surveys).

The usual practice is to quote WMAP+BAO+SNe figures, because based on all relevant data and considered most reliable.

No one should suppose that we are talking about the actual universe here. We are talking about best fit models. The values of the parameters that give the best fit to millions upon millions of datapoints.

Getting the mathematically simplest model that gives the best fit. This is what cosmology about, not verbal concepts or philosophy or even mental pictures, although pictures can help visualize the model.

If you are used to talking with people about Omega_tot, the total Omega**, it will help you make sense of Table 2 to know that
Omega_k = 1 - Omega_tot.

So the positive curvature case, the spatial closed universe, which has Omega_tot > 1, is the case where Omega_k < 0.
It is a quirk in the notation, positive curvature corresponds to Omega_k negative.

All standard cosmo models are edgeless in other words boundaryless. This is whether or not they are finite spatial volume. Boundaries would screw up the physics, add unnecessary complication, and provide no improvement to the data-fit. Almost the only finite volume case ever considered is the positive curved hypersphere. The 3D analog of the 2D balloon surface.

There is a rarely discussed flat model with finite 3D volume sometimes called "pacman" which is a cube with opposite sides equated so that running off thru the right wall makes you come in thru the left wall.

There is no sign of any such funhouse wall of mirrors stuff going on in the real universe so people normally ignore "pacman". Typically it's taken for granted that Omega_k = 0 means infinite 3D volume. This case, the flat infinite volume, is the easiest to calculate with and, since it provides a decent fit, widely favored. But the positive curved hypersphere case is not ruled out and may give a marginally (not statistically significant) better fit to the data.

*Here is the 95% confidence interval they give on page 4: −0.0179 < Ω_k < 0.0081
You can see it is tilted in favor of negative Omega_k, which means positive curvature, the finite volume 3D spherical case. But only by about 2 to 1.
Still not significant. Could go either way. A new spacecraft, the Planck, is planned for launch this year. Should further narrow down the limits.

**Omega_tot is the ratio of the total energy density, the measured largescale average density of all forms, divided by the critical density which the universe would need to have in order for space to be exactly flat. Omega_tot = 1 signifies the spatial flat case, zero curvature.
Omega_tot > 1 is the positive curved case where space is a 3D analog to surface of a sphere.
The critical energy density is easy to calculate from the Hubble rate H. It is simply 3c²H²/(8 pi G). If you ever want to know it, just type
3 c^2 (71 km/s per Mpc)^2/(8 pi G)
into google and it'll be calculated for you. If you like some other value of the Hubble rate, put that in instead of 71 km/s per Mpc.

This post has been edited by Martin: 25 January 2009 - 02:48 AM

[Martin]

Here's an alternative link to the "Misconceptions about the Big Bang" article from the March 2005 SciAm that has proven generally useful:
http://www.astro.pri...ionsBigBang.pdf

The one I've been using has a black page at the beginning of the pdf file, which might confuse people.
http://www.mso.anu.e...rDavisSciAm.pdf

[Martin]

It might sometime interest folks to look into the beginning of the expansion cosmo model.
Here's a facsimile of page 1 of Friedman's 1922 paper:
http://www.springerl...text.pdf?page=1

Here is a scan of the entire 10-page paper
http://edocs.ub.uni-.../E001554876.pdf

I see he makes a rough estimate of the age of the expansion---he says 10 billion years---gets it roughly right!

Friedman's work was not based on redshifts. An American astronomer Vesto Slipher had previously measured some galaxy redshifts but had not discovered their correlation with distance. Later on, Hubble was able to estimate distances and thus to correlate redshift with distance and find the linear proportion connecting them (Hubble's Law 1929).

It is interesting that the expanding universe idea came before the discovery of Hubble's Law. There is no indication that Friedman knew of Slipher's redshift measurements: he arrived at the expansion model on theoretical grounds, based on General Relativity (1915).

An English translation of Friedman's 1922 paper is here, but it is pay-per-view
http://www.springerl...rder=asc&p_o=10

Willem de Sitter came up with an expanding universe model in 1917. Here is a link to one of two papers he wrote that year:
http://www.digitalli...pdf=&var_pages=
Fortunately the paper is in English. The last page is missing in this free digital library copy. De Sitter seems to have a more abstract theoretical interest. I don't see him treating his model as a possible fit to reality. It is of interest as a possible solution to the equation of General Relativity, and an alternative to Einstein's static model. Friedman, on the other hand, plugs some real numbers in and makes a bold attempt to get a rough fit.

Neither of them seem aware of redshift information.

This post has been edited by Martin: 12 April 2009 - 01:12 AM

[Martin]

Questions keep coming up about the usual global time in cosmology. For example someone asks how can someone anywhere in the universe tell this time?

There are various ways, like measuring the temperature of the Background for instance. It declines as a predictable function of time, so you can tell time by it. Admittedly crude because temperature measurement is only so accurate, say to within one part per million. So your clock would only be accurate one part per million which is not very good. But its the concept.

Another way to tell universe-time is to measure the Hubble rate. This also is crude. It is around 71 currently. (The units they measure it in are an historical accident, not especially convenient, but that's how it is.)
I decided that I'd tabulate some expected future values of the Hubble rate.

  age   scale  estim. Hubble rate
13.7     1.00    71.0
14.1     1.04    69.0
14.6     1.08    68.2
15.1     1.11    67.5
15.6     1.15    66.9
16.1     1.20    66.2
16.7     1.24    65.6
17.3     1.29    65.1
17.9     1.35    64.6
18.5     1.40    64.1
19.2     1.47    63.7
19.9     1.54    63.3
20.6     1.615   62.9
21.5     1.70    62.55
22.3     1.79    62.25
23.2     1.90    62.0
24.2     2.02    61.7
25.2     2.15    61.5

The scale ratio is just how I'm keeping track of the expansion. The age is currently 13.7 (billion years) and by the time it is 24.2 longrange distances will have doubled, increased by a factor of about 2.02.
That means the Background temperature will be half what it is now.
2.728 kelvin/2.02 = 1.35 kelvin.

So if you should suddenly be transported to some other unknown location in the universe, and some other time in the future, and you want to know what time it is, then you can see all you need to do is measure the background temperature. If it is 1.35 kelvin then you know you have been transported to year 24.2 billion.

It's obviously absolute and it is based on general relativity---the Friedman solution to the basic GR equation.

Likewise if instead of measuring the temperature you look around and compare distances and redshifts and measure the Hubble rate (just like Hubble did) and if you find that it is 61.7 km/s per megaparsec (or whatever units the aliens on that distant future planet are using) then you can say immediately that you are in year 24.2 billion. It isn't especially accurate but you an tell the time by looking at the sky---whenever wherever in the universe.

This post has been edited by Martin: 2 May 2009 - 06:28 AM

[Martin]

One of the things that we should be able to calculate is the size of the observable, compressed to Planck density.

You should also be able to calculate the critical density from today's Hubble rate of 71 km/s per Mpc. It is about 0.85 nanojoules per cubic meter. If anyone wants to see the calculation please ask. It's easy.

The usual estimate of matter density is 0.27 of critical. So that comes to about 0.23 nanojoules per cubic meter.

What we need to know is the ratio of Planck density to that. The cube root of that ratio will be how much we shrink the radius of the observable.

Planck energy density ( http://en.wikipedia....ki/Planck_units ) is c^7/(hbar*G^2)

So we just type this into google:
(c^7/(hbar*G^2))/ (0.23 nanojoule/cubic meter)
We should get some huge number.

Yes! we get 2.0 x 10¹²³

The radius of the observable is currently 46 billion LY. It has to be shrunk by the cube root of that huge number. We should get something like the size of a proton, if I remember right. So let's take the cube root. Put this into google:
((c^7/(hbar*G^2))/ (0.23 nanojoule/cubic meter))^(1/3)

We get 1.26 x 10⁴¹.

So now let's shrink the radius of the observable by that factor. Put this into google:

46 billion light years/ (1.26*10^41)

What I get is 3.5 x 10^-15 meters.
3.5 femtometers.

The proton Compton wavelength is 1.32 femtometers.

Actually in the bounce cosmology models they find the bounce happens at some fraction of Planck density. So it wouldn't go quite that high and the size wouldn't be quite that small. But this is a good ballpark figure. You can interpret it by comparison with nuclear particle sizes however.

This post has been edited by Martin: 8 May 2009 - 11:45 PM

[Martin]

Here's how this thread began:

Martin said:

Before posting on cosmo topics consider getting squared away on the conventional standard version. There are several great tutorials, for which I'll post link. And the standard model universe is embodied in some online calculators---playing around with them gives you some hands-on experience with redshifts, recession speeds, distances and so forth...
...

It is not contrary to normal science practice to expect people to have a basic knowledge of the conventional standard theory, especially if they want to deviate from it, or go beyond it.

Nobody expects you to believe any particular theory.

Believe what you want. Criticize the standard model all you want too. But understand what you are criticizing.

We have an educational responsibility to explain the consensus cosmology that just about any professional cosmologist assumes as a working model.
Because when professionals talk and write they are assuming those concepts. And they are the most vigilant critics as well---you get extra respect points if you can find some observation that calls the standard model into question or suggests some needed modification.

A common point of departure is normal science practice. In fact that's the basic reason for this thread! :D

[DrRocket]

Martin, on 11 May 2009 - 02:22 AM, said:

Here's how this thread began:

It is not contrary to normal science practice to expect people to have a basic knowledge of the conventional standard theory, especially if they want to deviate from it, or go beyond it.

Perhaps this can help those interested in delving into cosmology at some depth.


The pillar of modern cosmology is one of the pillars of modern physics, general relativity.

General relativity (GR) was formulated by Albert Einstein and announced in 1915. It has since received a great deal of attention, the mathematical foundations have been examined, the presentation refined, and a host of confirming experiments performed. General relativity, with its mathematical roots in Riemannian geometry is a formidable subject, and some of its predictions are contrary to everyday experience – i.e. “common sense” can be badly mistaken. That is no surprise as even special relativity, the precursor and “little brother’ of GR is surprising at first encounter.

http://math.ucr.edu/...baez/gr/gr.html
http://en.wikipedia....eral_relativity
http://en.wikipedia....eral_relativity
http://rspa.royalsoc...1732/5.full.pdf

GR treats the universe over all time as a single entity – spacetime. This can also be done in Newtonian mechanics, so there is nothing really new about spacetime. What distinguishes GR is that spacetime is not just affine 4-space, but in fact is a Lorentzian 4-manifold of undetermined topology, with a curvature tensor that is also unknown but is determined by the distribution of mass/energy via a stress-energy tensor defined by a very complex set of partial differential equations. These equations, the Einstein field equations can only be explicitly solved in a few simple circumstances. Gravity is the result of curvature of spacetime.

In general because of curvature neither space nor time have any global meaning. However, if one makes the assumption that spacetime is homogeneous and isotropic, then spacetime decomposes as a 1-parameter foliation by space-like 3-dimensional hyperplanes of constant curvature. The parameter serves as a surrogate for time and the hyperplanes as a surrogate for space. The hyperplanes inherit a true Riemannian metric from spacetime and expansion of space means that the distance between points increases as the value of the time-like parameter increases.

Astronomical observations support the assumption that the universe is homogeneous and isotropic on the largest scales. Observations also support the expansion of space.

http://scienceworld....leConstant.html
https://www.cfa.harv...~huchra/hubble/
http://map.gsfc.nasa..._expansion.html
http://map.gsfc.nasa.gov/
http://en.wikipedia....nisotropy_Probe
http://aether.lbl.go...cience/cmb.html
http://aether.lbl.go...cience/cmb.html

Based on these assumptions and observations Hawking and Penrose in a series of papers used general relativity to conclude that, as a logical consequence, the universe began in an extremely compact form, and in fact predicted singular behavior (which is generally thought to indicate a limitation of general relativity to predict the first fraction of a second)

http://web.archive.o...ing_text.shtml/
http://rspa.royalsoc...b7-91869da35ea6
http://rspa.royalsoc...b7-91869da35ea6
http://rspa.royalsoc...b7-91869da35ea6
http://rspa.royalsoc...9.full.pdf+html

So, while nobody knows what happened in the first fraction of a second, the big bang hypothesis in terms of subsequent expansion from an extremely compact state is on firm empirical and theoretical grounds.

Inflation is not necessary to the big bang, but does use ideas from quantum field theory to explain why the universe is homogeneous on the large scale, yet exhibits anisotropy on smaller scales. It is not a fully verified, or even rigorously formulated, theory, yet. It is promising. It is supported by what has been seen in surveys of the cosmic background radiation. Attacking inflation as unproven is futile, because it is well-known to be just that. But interpreting “unproven” as fanciful or unlikely is simply a demonstration of ignorance.

http://web.mit.edu/p...2_cosmology.pdf

Thus, modern cosmology rests on a solid foundation of empirical data and well-formulated theory. That does not make it immutable. Any physical theory is subject to refinement and extension. But any revision must meet equal standards of rigor.

Anyone who rejects modern cosmology must meet the obligation of providing the basis for an alternative . That means providing a theory of gravity to replace GR, and the empirical data to support it. Further, that data must include ALL valid data, including that which currently provides evidence for the validity of GR itself.


Addendum: useful references for the serious (these are NOT popularizations)

Gravitation -- Misner, Thorne, Wheeler

Gravitation and cosmology : principles and applications of the general theory of relativity -- Weinberg

Cosmology -- Weinberg

General Relativity -- Wald

Principles of Physical Cosmology -- Peebles

The large scale structure of space-time -- Hawking and Ellis

General Relativity and the Einstein Equations -- Choquet-Bruhat

[ryellen4ar]

thank you for sharing