The water beetle was sent on an exploration, and after darting about on the surface and finding no rest, it dived down to the depths, whence it brought up a bit of mud, from which the earth grew by accretion.
Apache Creation Myth
In what follows:
The smallest things we will talk about are galaxies:
typically 10 billion (1010) stars and a size of 20 kpc (1020 m)
M51 in Can Ven: HST picture
But most of the time we'll be talking about clusters of galaxies: this is VIrgo.
typically 1 million billion (1015) Msun and a size of 2 Mpc (1022 m)
Redshift:
In 1928, Slipher-Hubble-Humason found light from most galaxies is redshifted.
The Doppler effect gives z = (λ-λ₀)/λ₀ = Δλ/λ₀
Velocity of recession: v = zc = Δλc/λ₀
Hubble
found vel. of recession ∝
distance \color{red}{v = Hd,H = 70{\rm{ km/s/Mpc}}}
1 Mpc (megaparsec) = 3x1022 m.
Note although all galaxies are receding from us, does not imply we are at the centre: in the currant cake model all currants see all the others as receding
Must be age of universe: if expansion does not change
i.e. 17x109 yr. ago, all the galaxies were in the same place. Universe had a beginning, implied by the big bang. Can run Hubble expansion back: we would like to use this to predict what will happen in the end
Where was the Big Bang?
A 2-D analog is the surface of a balloon: Note the following:
It has no centre in 2-D space.
Deflating it reduces it to zero size: i.e. at the moment of the big bang, not only matter was created, but also space and time
The galaxies are not receding from us: space is expanding
We require a curved 2-D surface embedded in a 3-D volume.
We can define coords on the balloon that will expand along with it: this is a "co-moving" system
This is a positively curved universe: we can also construct negatively curved ones (harder to visualize)
What's going to happen in the end?
The sky becomes black, Earth sinks into the sea From Heaven fall the bright stars The sea ascends in storm to Heaven It swallows the Earth, the air becomes sterile
From the Hyndluljod (Iceland)
How can we tell if the universe will expand forever?
As a model, consider this as an escape velocity problem. How hard do we need to throw a galaxy on the "outside" so that it escapes? Note: our calculation had better not depend on r!
(we got lucky: the r cancels out!). We can turn this round and write it as an equation for ρ
\color{red}{
\rho _0 = \frac{{3H^2 }}{{8\pi G}}}
Hence the critical density
ρ₀ ~ 9 x 10-27 kg m-3 ~ 6 Hydrogen Atoms m-3 (Number is flaky). We'll use \color{red}{\Omega {\rm{ = }}\frac{\rho }{{\rho _0 }}}
, because some errors cancel out.
The entire future of the universe is given by this one number!!!!!!!!!
(and isn't it nice that the end of the universe is defined by Omega Ω!)
So if
Ω > 1
Universe come to nasty end in ~ 50 x 109 yr.
More important:we live forever if Ω ≤ 1, (well maybe).
So how do we weigh the universe?
There is still a big dark mystery out there
There is only a single God, Mixcoatl, whose image they possess, but they believe in another, invisible, god, not represented by any image, called Yoalli Ehecatl, That is to say, God Invisible, Impalpable, Beneficent, Protector, Omnipotent by whose strength alone...rules all things
Nahuatlan Myth
Can only see luminous matter: how much Dark Matter is there?
Usually expressed as mass to luminosity ratio, relative to the sun.
First Guess: What you see is what you get!
Count number of galaxies in a region of space, assume they consist of stars much like the sun, so assume
\color{red}{
\frac{M}{L} = \frac{{M_o }}{{L_o }}}
Obviously must average over large enough volume such that universe is smooth R > 100 Mpc, and the universe is a very lumpy place!
=> Density:
\color{red}{
\Omega \approx .002}
(Note all these numbers are uncertain to ∼ 20%!)
We live forever!!!
But wait a moment...
How much matter is there we that we can't see? This assumes ρdm ~ 0
Masses of Spiral galaxies
direct observation i.e. measurement of velocities of individual stars in nearby => rotation curves or measurement of hydrogen via 21cm line or estimates of no. of stars
Typical Spiral (NGC3198) R ≈ 20 kpc but outer parts are just seen as H gas
Luminosity of galaxy should reflect mass
Most of the light is fairly concentrated, so this should be good approx to the mass.
but the outside part of the galaxy is rotating far to fast: i.e. velocity curve doesn't drop as expected. Means a lot of mass in outside part of galaxy
b) Why the hell? i.e. why is Ω~1 (after all it could be anything?)
Actually, there is a limit
Ω < 3
otherwise the universe would be younger than the earth (wouldn't that make the creationists happy!!)
What the hell:
Brown dwarfs
Hydrogen gas
Jupiters
Hydrogen rain
Low surface brightness galaxies
Maxi Black holes
Mini Black holes
Neutrinos
He H +
Modified 1/r² law
Axions
Weakly Interacting Massive Particles (WIMPS)
Magnetic Monopoles
Majorons
Photinos
E8 shadow matter
Cosmic Strings
Which is it? We don't know! However, all of the above have problems.
The Generic Candidates for Dark Matter :
Baryonic (BDM): (we use this as shorthand for "ordinary matter") maybe in some odd form e.g. rocks
Hot (HDM) light particles e.g. ν's
Cold (CDM): heavy (usually) particles e.g. WIMPs
What the hell:
Brown dwarfs Not enough
Hydrogen gas Would be seen unless it was very diffuse, in which case, not enough
Jupiters Not enough
Hydrogen rain Too hot
Low surface brightness galaxies Doesn't fix the problems in spirals
Maxi Black holes Only exist at the centre of galaxies: we need halos
Mini Black holes Not enough
Neutrinos Part of the solution, but too light
He H + Unstable
Modified 1/r² law Hard to reconcile with Bullet cluster
Axions Negative searches so far
Weakly Interacting Massive Particles (WIMPS)
Magnetic Monopoles Screw up magnetic fields in galaxy
Majorons
Photinos Will see them in 2008 (maybe)
E8 shadow matter and there is a tooth fairy...
Cosmic Strings
No-Nameons: CDM candidates
Axions
Majorons
Weakly Interacting Massive Particles
Photinos
LSP's (Lightest Supersymmetric Particles)
Magnetic Monopoles
E8 shadow matter
Although these are similar cosmologically, they are very different from the point of view of detection.
WIMPS
A lot can be ruled out by "in vitro" experiments (e.g. OPAL: Richard Hemingway and others at Carleton) at CERN
ATLAS (2008: Manuella Vinctner and 1500 others) will be able to rule out a lot more option (any reasonable with m < ∼ 1TeV)
Generic WIMPS can be seen "in vivo" via a variety of low temp. expts.
e.g. Queens-U de Montreal Picasso expt. Nucleus will recoil and transfer energy to super-heated freon liquid and cause transition to gas.
In solid, nucleus will recoil and transfer energy to lattice, flipping superconductor or sending off ballistic phonons. DEAP (Kevin Graham): will use 1 tonne of liquid argon.
Where did the galaxies come from?
There is confirmation of the general CDM/WIMP picture from the microwave background measurements: fossil light shows us what the universe was like 300,000 years after the Big Bang
COBE and WMAP comparison
Before galaxies form, Universe is filled with fluid of radiation and matter.
Normally density fluctuations die away (e.g sound waves) but in massive fluid they get amplified by gravity
Hence Scenario
CDM decouples
CDM dominates and clumps
Atoms (baryons) decouple
Baryons clump onto CDM
Galaxies form
Dark Energy
And just when you thought it was safe to go out at night....
Dark Matter is bad enough, but now dark energy ...
Luminosity distance "standard candle"
If Luminosity is known, then flux is
\color{red}{
f = \frac{L}{{4\pi d_L^2 }}}
Type 1a Supernovae Mv = -20 allows us to measure out to 3000Mpc
Hence importance of 1a supernovae: since we know (maybe) L, we can get $q_0$ directly.
CFHT
Canada-France Hawaii Telescope (CFHT)
SuperNova Legacy Survey
(U of T and others) now provides best data from CFHT
implies a cosmological constant Λ (Einstein's "fudge factor"): in other words vacuum has an energy.
What can dark energy be?
List of all well-motivated models for dark energy
-
-
-
-
-
The implication is that the expansion of the universe is accelerating: q₀,< 0(!)
Combining this with data from WMAP gives
so finally
ΩM = 0.27 ± .02
ΩΛ = 1 - ΩM
w = -1.02±.1
This gives a "best guess" due to Michael Turner
note that ν is highly uncertain: could be massless, could have m = 1eV
However, there are major problems (what, more?).
Dark energy implies that the vacuum has an energy density: $$
\color{red}{
\rho _\Lambda \approx 100\rho _B \approx 10^{-13} JM^{ - 3} }
$$
We could understand ΩΛ ≡ 0. : but....
The only working theory for particles (the standard model) gives \color{red}{
\Omega _\Lambda = 10^{110} - V_0
}
where V₀ is a (unknown) correction. You will notice a discrepancy!
All of this depends on the assumption that type 1a SN are always the same at 4x109 Lo, even at z = .5. Effect disappears if some (unknown) effect reduces L by 30%
e.g. SNLS has found one very odd SN: 03D3bb
e.g. Hubble original estimate for H0 was wrong by factor 7 because 2 different kinds of Cepheids.
Dark energy essentially requires negative pressure.
Secondly, ΩΛ and ΩMatter are almost equal at present. In the past they would have differed by 1040
Some models suggest the universe will accelerate out of control ⇒ Big Rip in ∼ 35 *109 years
we have no theoretical estimate for ΩΛ
However, combined with WMAP and other results, ΩΛ ∼ .74 seems likely to be correct
Summary
So......
We need dark matter
We need ΩDM ∼ .26
We know Ωbaryons ∼ .03
We have quite reasonable models for DM
We will (likely) see it by 2010
If we don't we'll have eliminated a lot of models
We seem to require dark energy
We need ΩΛ ∼ .74
We have no good models
The good models we do have predict nothing like the values we see