Warning: jsMath requires JavaScript to process the mathematics on this page. If your browser supports JavaScript, be sure it is enabled.

Cosmology Introduction ...or... Physics as a Creation Myth

NASA, ESA, Hubble Heritage Team (STScI / AURA) Acknowledgment: J. Blakeslee (Washington State University) Galaxy cluster Abell S0740.

`I can't believe THAT!' said Alice.

`Can't you?' the Queen said in a pitying tone. `Try again: draw a long breath, and shut your eyes.'

Alice laughed. `There's not use trying,' she said: `one CAN'T believe impossible things.'

`I daresay you haven't had much practice,' said the Queen. `When I was your age, I always did it for half-an-hour a day. Why, sometimes I've believed as many as six impossible things before breakfast. '

A Creation Myth???????????

In the beginning the Universe was created. This has made a lot of people very angry and has been widely regarded as a bad move. Many people believe that it was created by some sort of God, though the Jatravartid people of Viltvodle Six firmly believe that the entire Universe was in fact sneezed out of the nose of a being they call the Great Green Arkleseizure.
The Jatravartids, who live in perpetual fear of the coming of a time that they call The Coming of the Great White Handkerchief, are small blue creatures . However, the Great Green Arkleseizure theory was not widely accepted outside Viltvodle Six, and so one day a race of hyper-intelligent beings built themselves a gigantic computer called Deep Thought to calculate once and for all the answer to the Ultimate Question of Life, the Universe and Everything.
which was, of course,

42.

From "The Hitchhiker's Guide to the Galaxy", Douglas Adams

Ingredients for a creation myth:

Doesn't it make you feel humble!
So how did it all begin?
What's going to happen in the end?
There is still a big dark mystery out there.
Things were so much simpler back then
Fortunately, there is a special place for us.
But what happened before?
What a beautiful story!

Cosmology 1: Doesn't it make you feel humble!

Space is big. Really big. You won't believe how vastly, hugely, mind-bogglingly big it is.

Hitchhiker's guide to the Galaxy.

How big is the universe?

How big? Could it be infinite? A much harder problem that you might think!
Distances to Galaxies: Steps out from earth,
Astronomical unit≈10¹⁰m 10 billion m or 8 light-minutes
Parallax of Individual stars (Aristotle had problems with this!) 10¹⁸m ∼ 100pc

Cepheids: supergiant stars which pulsate regularly, can be seen in M100

20 Mpc

Credit: NASA, HST, W. Freedman (CIW), R. Kennicutt (U. Arizona), J. Mould (ANU)

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) M_sun and a size of 2 Mpc (10²² m)

Olber's Paradox

Why is the sky dark at night?

If universe is

infinite

uniformly filled with stars

Any line of sight will end on a star, so night sky will be bright
But it isn't !

Apparent Ways out:

Obviously universe is not uniform for stars
But it is for galaxies
Light from stars falls off as inverse square law (1/r²)
But the number of stars increases as r² so the effects cancel

Absorption by interstellar matter dims distant stars
But the matter would by now be hot and radiating
Light is redshifted to very long wavelengths so objects within ~ 3000 Mpc will have any visible radiation at all
But this implies that the universe must be expanding

Very distant objects would correspond to an age of more than 10 billion (10¹⁰) years
No reason why the universe should be the same then

Hence an expanding universe with a beginning is almost required by Olber's Paradox: it cannot be infinite in both space and time.
Cosmological Principle: All observers see roughly the same universe, i.e.universe is isotropic.
Obviously this is not true on a small scale!
Atoms => Stars => Galaxies=> =>Clusters=>Superclusters
At each stage the distribution becomes more regular, and finally there is no evidence that superclusters clump
Note: this is a hope, not even an observation!

Doppler Effect

Waves coming from a moving source have their frequency and wavelength changed. Watch the animation.

Doppler effect gives

\color{red}{ z = \frac{{\lambda - \lambda _0 }}{\lambda } = 1 - \frac{{{\rm{original wavelength}}}}{{{\rm{measured wavelength }}}}{\rm{ }}}

Vel. of recession

\color{red}{ {\rm{v = zc = c}}\left( {\frac{{\lambda - \lambda _0 }}{\lambda }} \right)}

This formula isn't quite right: we can have z > 1: in fact the furthest known galaxy has z = 4.9. We have to use a relativistic formula in that case.

Found in 1920's (Hubble, Humason, Slipher) that faint galaxies show a red shift: fainter the galaxy, faster the recession.

So how did it all begin?

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

Hubble was able to measure distances to closer clusters and found that velocity ∝ distance

\color{red}{ v = Hd}

H is Hubble constant: As measured by Hubble H = 550 km s^-1/Mpc: Now we know

H ~ 70kms^-1/Mpc

1 Mpc (megaparsec) = 3x10²² m

i.e. the average galaxy at 100 Mpc is receding at 6500 km/s

Big Bang (once over lightly)

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 recediing

RULE 1 in Physics 100: Never mix your units!)

\color{red}{ v = zc = Hd,H = 70.1 \pm 1.3{\rm{km s}}^{{\rm{ - 1}}} {\rm{Mpc}}^{{\rm{ - 1}}} }

so \color{red}{ H = \frac{{70.1 \times 10^3 }}{{3.1 \times 10^{22} }} = 2.26 \times 10^{ - 18} s^{ - 1} }

We can invert this to give

\color{red}{ H^{ - 1} = 4.4 \times 10^{17} s = 14 \times 10^9 yr}

What does this time represent?

Must be age of universe: if expansion does not change

i.e. 14x10⁹ 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.

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)

Will 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!
\color{red}{ \frac{1}{2}mv^2 - \frac{{GMm}}{r} = 0}
but \color{red}{v = Hr}
and the total mass of the universe inside \color{red}{M = \frac{{4\pi }}{3}\rho r^3 }

so...

\color{red}{H^2 r^2 = 2G\frac{{4\pi }}{3}\rho r^2 } (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 \color{red}{ \rho _0 = 9.2 \times 10^{ - 27} kgm^{ - 3} \sim 5.5 } H atoms m^-3 (Number is slightly flaky).
Will mostly use \color{red}{\Omega = \frac{\rho }{{\rho _0 }}} because some errors cancel out. The entire future of the universe is given by this one number!!!!!!!!!
I am the Alpha and Omega, the Beginning and the End, saith the Lord. Revelations I v7.

So if

Ω > 1 Universe come to nasty end in ~ 50 x 10⁹ yr.
Ω = 1 Universe expansion slows down asymptotically : "critical universe"
Ω < 1 Universe expands forever
More important:we live forever if Ω ≤ 1, (well maybe).

Note that this implies that the rate of expansion must change

Gravity will slow down expansion in the early stages, so Hubble's constant isn't a constant... when the universe was smaller, v was larger so H must have been bigger. Better "the Hubble parameter"

From this (incredibly naive) model we can deduce:
Density
Expansion time
Temperature of the universe
Corrections if the density is not critical

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

So how do we weigh the universe?
Can only see luminous matter
How much Dark Matter is there?

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 \color{red}{\upsilon = \frac{M}{L} \approx \frac{{M_ \odot }}{{L_ \odot }}}

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 _M = \frac{{\rho _M }}{{\rho _C }} \sim .001}
(Note all these numbers are uncertain to ∼ 50%!)
We live forever!!! But wait a moment...
How much matter is there we that we can't see? This assumes ρ_dm ~ 0

Note that although we always show dense bits of the universe there are a lot of voids out there. The biggest void here is 650 Mpc across: no more than a dozen galaxies (each dot is a galaxy: "picture" is slice of universe out to 1.5 Gpc

But maybe there is some dark matter we can't see....

Masses of Spiral galaxies

Measurement of velocities of individual stars or clouds of hydrogen (via 21cm line) ⇒ rotation curves
Typical Spiral (NGC3198) R ≈ 20 kpc
but outer parts are just seen as H gas

Luminosity of galaxy should reflect mass: brightest at centre, so most of mass should be there.
Most of the light is fairly concentrated, so this should be good approx to the mass.
Just like Newton measuring mass of Jupiter via Io's orbit ⇒ predicted rotation curve.
but velocity curve doesn't drop as expected

Can fix this by saying that galaxy has halo of dark matter around it.

Halo + core add together to give correct curve

But the halo has to be 40x more massive than the visible galaxy....!
i.e. the stars represent a tiny amount of the mass in a galaxy. What is the rest?

Note this is not unique to NGC 3198: all measured spirals show same.

Large clusters of galaxies:

Can measure speeds of individual galaxies in a cluster:
faster moving galaxies imply more mass in cluster
This gives much higher masses than individual spirals
300 times more invisible matter than visible .....!

A check: The Coma cluster

Large clusters contain a lot of hot gas, which is strong X-ray source. (Picture is negative optical + contours of X-rays) X-ray pictures measure density and temp:
but the X-rays don't come from where the matter is .....

Also large masses bend light, so large clusters show "gravitational lensing" of very distant objects.

Allows us to estimate the mass. For Abell 2218 we seem to have at least 300 times as much dark matter as luminous matter

a) What the hell? i.e. what is the dark matter?
b) Why the hell? i.e. why is Ω~1 (after all it could be anything?)
Actually, there is a limit \color{red}{\Omega < 3} , otherwise the universe would be younger than the earth (wouldn't that make the creationists happy!!)

6) Things were so much simpler back then

It is believed that the first nine inhabitants who had descended from the skies were sexless and sinless and lived on a kind of flavoured earth. Their appetites grew and when they took to eating a sort of huskless rice which cooked itself they became gross and heavy, developed sex and after it crime because they had to work for a living
Kachin Myth

Cosmic Microwave Background Radiation

Early universe must have been very simple: there can have been no stars or galaxies.

However, it was very hot: hot things radiate....
Universe is "full" of light: fossil light from Big Bang, discovered accidentally by Penzias and Wilson (1964)
Found that "noise" came from universe independent of what angle horn was pointed in: corresponded to a black-body temp of 3⁰K
Have to get above atmosphere and point away from Milky Way.

Have to get above atmosphere and point away from Milky Way

Subsequent values came from balloon flights:

Finally COBE (Cosmic Background Explorer: 2006 Nobel Prize for Mather and Smoot) launched 1990:

Note the perfect Black Body curve.

Where does it come from?

Gamow (1948) discussed Hot Big Bang for first time, suggested that E.M radiation from it should still be observable.
Peebles (1964) had calculated that it should be observable, but thought T ~ 10 ⁰K, (and everyone had general feeling that it would be unobservable).
This is often the way it is in physics: our mistake is not that we take our theories to seriously, but that we do not take them seriously enough. It is hard to believe that the numbers that we play with at our desks have something to do with the real world. Steven Weinberg The First Three Minutes

This "light" is now at 2.736°K, and almost uniform in every direction. It was emitted just 500000 years after the Big Bang and has been travelling round the universe ever since.
As the universe expands, the density of γ's decreases. and also the temperature T falls as each γ gets redshifted.

Photon freezeout:

CMBR must be linked to the matter in the universe
Initially matter and radiation are in thermal equilibrium(at the same mean energy) with a Black Body distribution of γ's.
Expansion ⇒ Cooling.

The universe was originally opaque, like a fog, so mean free path of γ's very small. Hence CMBR was at same temp as matter. Then the universe became transparent and photons "froze out."
photon "freezeout" occurred ≈ 400000 years after the Big Bang
Photons have been travelling ever since, so this is the oldest thing we can see ....

More exactly

Photon density N ≈ 10⁹ m^-3
Temp. of the microwave sky in a scale in which blue is 0 K and red is 4 K. Note completely uniform on this scale. The actual temperature of the cosmic microwave background is 2.725 Kelvin.

If we are moving through CMBR we would expect to see it "warmer" in front and "colder" behind.

Blue ↔2.721 Kelvin
Red ↔2.729 Kelvin

so CMBR is blue-shifted in the direction we are going in (note residual effect of galaxy): what do we expect for 600 km/s?
Credit: DMR, COBE, NASA, Four-Year Sky Map

shows we are moving towards Leo at≈ 606 km/s

So need a new satellite: WMAP: COBE and WMAP comparison. Indicates that the universe was very uniform back then. Hotter where it is denser, and this shows where the galaxies should be forming Can just see structure at: ΔT/T ≈ 10^-6.

Unfortunately, well-formed galaxies are there at t ~ 3x10⁹ yrs.
How did the galaxies form so quickly between one million yrs (when there are no indications) and one billion (when they are well formed and look like today's galaxies)?
Seeds must have been there ⇒ temp fluctuations.

So what is this Dark Matter?

a) What the hell? i.e. what is the dark matter?

b) Why the hell? i.e. why is Ω~1 (after all it could be anything?)

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. neutrinos.
Cold (CDM): heavy (usually) particles e.g. WIMPs

The Bullet Cluster

Combination of lensing (blue) and X-rays (red) in the bullet cluster:

Strong evidence for non-interacting dark matter:

X-ray emitting material is gas, so gets stopped in collision
dark matter gets carried along

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
~~E₈ shadow matter~~ and there is a tooth fairy...
~~Cosmic Strings~~Form in wrong place
~~Magnetic Monopoles~~ Screw up magnetic fields in galaxy
Weakly Interacting Massive Particles (WIMPS)
e.g. Photinos Will see them in 2008 (maybe)

WIMPS

Seem like the best bet.... Generically behave like very heavy neutrinos.

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 at Carleton 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.
e.g. DEAP (Kevin Graham at Carleton

Where did the galaxies come from?

There is confirmation of the general CDM/WIMP picture from the microwave background measurements:

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
So you exist because the CDM dragged together the matter.

Can simulate structure formation with (massive) n-body codes (n = 10⁷ gravitating objects): on the large (super-cluster) scale. Note that we get a sort of stringy structure, which looks like what we observe

Or on scales of galaxies.

{Performed at the National Center for Supercomputer Applications by Andrey Kravtsov (The University of Chicago) and Anatoly Klypin (New Mexico State University).

Why the hell?

b) Why the hell? i.e. why is Ω~1 (after all it could be anything?)

At any time, critical density is given by

\color{red}{ \rho _0 = \frac{{3H^2 }}{{8\pi G}}}

and

\color{red}{ \Omega {\rm{ = }}\frac{\rho }{{\rho _0 }} = \frac{{{\rm{actual\_density}}}}{{{\rm{critical\_density}}}}}

If Ω < 1, then it decreases away from 1.
If Ω > 1, then it increases away from 1.
If Ω = 1, then it stays 1 forever

This is the "flatness problem": i.e. Ω = 1 is an unstable critical point.

Think of a pencil
Stable equilibrium is lying flat (Ω = 0 or Ω = ∞)
Unstable equilm is balanced on the point: (Ω ≅ 1)
But you can't have it at 30° (say Ω = 0.999 or Ω = 1.001)

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 we can get the distance:

Type 1a Supernovae Mv = -20 allows us to measure out to 3000Mpc

CFHT

First results from Supernova Cosmology project, Now Canada-France Hawaii Telescope (CFHT) (U of T and others) provides best data

SuperNova Legacy Survey

Obviously the universe is slowing down (decelerating).
Hence importance of 1a supernovae: since we know luminosity, we can get Ω_matter directly.
Unfortunately it isn't.....
It's speeding up

Only way we can get this to work is to add an accelerating component to the universe: something that adds energy as the universe expands, so vacuum has an energy.

Cosmological constant Λ (Einstein's "greatest blunder"):

What can dark energy be?

List of all well-motivated models for dark energy

A final note

There have been 3 scientific revolutions, all devastating for man's dignity.

Copernicus: We are not the centre of the universe
Darwin We are no different from the animals
Dark Matter/Energy: We are not even made of what most of the universe is made of! (but that means we are special!)

Anthropic Priniciple

Warning: for the rest of this course, you are on the hairy edge of science!

6) Fortunately there is a special place for us
And God said " Let us make man in our own image, after Our likeness, and let them have dominion....over all the earth Genesis I.26
Not only is this the best of all possible worlds, it is the only (observable, ) of all possible universes.

Relatively small number of parameters describe universe

Parameter	Value	Definition	Measured	Comments
G	6.673x10^-11	Grav. const	Lab	Newton
c	2.998x10⁸	Speed of Light	Lab	Rohmer
α	1/137	Strength fo EM coupling	Lab	Maxwell
m_ec²	511 keV	Electron mass	Lab	Thomson
m_Pc²	937 MeV	Proton mass	Lab	Chemistry/Rutherford
m_nc²	939 MeV	neutron mass	Lab	Chadwick
H₀	70±7 km s^-1Mpc^-1	Hubbles constant	Hubble
T_CMBR	2.726K	CMBR temp	COBE/WMAP
Ω_B	.03±.01	Nucleon density	WMAP, nucleosynthesis	Baryon density
Ω_{γ & ν}	3.4x10^-5	CMBR + BBN		Uncertainty due to ρ_c, assumes m_ν = 0
Ω_dm	.26±.02	CDM density	Spirals/Galaxy clusters
Ω_Λ	0.74	Curvature energy	Sn 1a
Ω₀	1.01±.02	Total energy

Anthropic Principle:

We've missed a few constants, but there are enough here so you can design a "Build Your own Universe" kit

Where do they come from?
Weak Anthropic Principle:
We see the universe the way we do because locally it is suitable for our existence
Strong Anthropic Principle:
The laws of the universe are such that it can become self-aware
Methodological Anthropic Principle ...the 'fine-tuning' is only apparent, not fundamental. i.e., given that we happen to be observing an observable universe (only one of all possible universes), the apparent 'fine-tuning' is nothing more than a consequence of the LAP
Teleological Anthropic Principle (Barrow and Tipler)
...the universe is habitable SO THAT intelligent life can evolve. i.e., habitability is the goal of the universe. The universe exists to support intelligent life!
=> Strong Anthropic Principle
Extremely Strong Anthropic Principle:
The universe exists to produce ...PHYSICISTS!

e.g.How old is the universe?

Physicists are made of carbon,
Carbon is not made in the big bang.
The universe cannot become self-aware until the first stars have completed their life-cycle.
Age of Universe > 1 Billion years

e.g. Could the forces in nature be any different?

Nuclei exist because of subtle balances between
1. Repulsive Electric Force
2. Attractive Nuclear Force
For heavy nuclei, (1) overwhelms (2), so they are unstable. If the electromagnetic force were 10% stronger
Then no nuclei except hydrogen would exist,
so no chemistry
so no biology
so ....NO PHYSICISTS!

if the electromagnetic force were 10% weaker
Then the di-proton is stable,
No hydrogen left over, so no water <
so no biology
so ....NO PHYSICISTS!

e.g How Dense is the Universe?

Low Density (e.g., Ω_i < 1-10^-60)
Universe Expands too fast
no Galaxies
no stars
no planets ...NO PHYSICISTS!
High Density(e.g., Ω_i < 1+10^-60)
Universe forms clumps
But collapses back to Big Crunch much too early
No time to evolve life ...NO PHYSICISTS!

But the Goldilocks Universe:
Critical Density Ω = ρ/ρ_c = 1
Just lumpy enough to make galaxies
and hence stars
And ...PHYSICISTS!

Anthropic arguments extend all the way from the physical constants and the masses and charges of the fundamental particles, to the gross properties of the universe...

Is this a reasonable scientific theory?
The anthropic principle gives little or no room for making predictions, upon which to conduct tests. The teleological principle verges on theism.
But: can we construct a universe which "works" with different parameters?
who says C-based life is the only possibility?
Hope now is find out what produces "complex" universes

7) So what happened before?

Then was not non-existent nor existent
There was no realm of air, no sky beyond,
What covered in and where? and what gave shelter?
Who verily knows and who can here declare it
Whence it was born and whence came this creation
He, the first origin of creation,
whether he formed it all or did not form it.
He verily knows it, or perhaps he knows not.
The Rig Veda X.129 (Hindu)

What happened before the Big Bang?
There is a special hell reserved for people who ask that question. George Gamow

Maybe the universe bounces
Cannot conserve energy (or more precisely, entropy increases every bounce).
2nd Law of Thermodynamics leads to: For a closed system (eg the universe?), entropy (degree of disorder) always increases towards a maximum, and energy always decreases towards a minimum.
Is the universe a closed system?

Continuous Inflation (Linde, 1990)

Any part of our universe could achieve the conditions required to trigger inflation. Hence it could give rise to a new "daughter universe". ...Our Big Bang is only for our region of the universe...

Implies you can create universe ex nihilo!
Why does the universe get created?
Universes tend to happen from time to time!

Note a hidden assumption in all of this:

Space, time and matter came into existence at t=0, but the rules were the same. Could the rules have been different?
Sakharov (1985) suggested that the rules of physics need not be the same in going from one universe to the next: (e.g.) the gravitational coupling could be set arbitrarily in the first 10^-30 s. If so, we could have a universe which is almost inconceivably different
Note (not for the first time) a failure of language: if the universe is everything, we can't talk about many universes. Hence the multiverse
Which takes us to...

Superstrings and the like:

We have seen that gravity curves space: in a sense, this is going to a larger number of dimensions.

Kalusza-Klein showed that one could include electromagnetism along with gravity by adding a fifth dimension, but making it compact
To include all the other forces in nature (strong and weak) we need to go to a 10-dimensional space.
You hadn't noticed that the universe is 10-D tsk-tsk.......
6 of the dimensions are compact (R ≈ 10^-33 m), and can be multiply-connected (i.e. can be toroidal or dough-nut shaped).
All particles (quarks, photons, electrons.....) are 2-D strings in this 10-D space.

For the first 10^-38 s the universe contained....
Nothing! No forces, no particles! Nada!
If we have more dimensions which fold up on themselves, is there any particular reason that the "compactification" is unique
Then the extra dimensions curled up and became compact
=> Forces => Particles => Atoms =>
...PHYSICISTS!
Unfortunately string theory gives 10⁵⁰⁰ possible universes

Statutory Warnings/To-do list

we need to have some other observation that tells us if the universe is accelerating
e.g. Hubble original estimate for H₀ was wrong by factor 7 because 2 different kinds of Cepheids.
Dark energy essentially requires negative pressure.
Ω_Λ and Ω_Matter 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 need dark matter: Ω_DM ∼ .26. We have quite reasonable models for DM and will (likely) see it by 2010. If we don't we'll have eliminated a lot of models
We know Ω_baryons ∼ .03
We seem to require dark energy Ω_Λ ∼ .74 seems likely to be correct
we have no theoretical estimate for Ω_Λ
The good models we do have predict nothing like the values we see, and may not know anything more for 20 years.
We need to know if we can construct other working universes.
We need to have some evidence for extra dimensions.

And so finally

8) What a beautiful story!

In the beginning, God created the heaven and the earth. And the earth was without form, and void; and God realised that this was not a very good way to start, so God said, Let there be a reinitialisation, and because God was God, he was able to start over.
In the beginning, God created the heaven and the earth. And the earth was without form, and void; and darkness was upon the face of the deep. And the spirit of God moved upon the face of the waters.
And God said, Let there be light, but God had forgotten to create electromagnetic interactions, so there was no light, so God said, Let there be a reinitialisation, and because God was God, he was able to start over.
In the beginning, God created the heaven and the earth. And the earth was without form, and void; but this time God decided to leave himself plenty of room for manoeuvre, so he created the heaven and the earth to have ten dimensions.
But then God realised that this was a very complicated way to run a universe, so God said, Let there be a reinitialisation, and because God was God, he was able to sta.....
But God had forgotten shlosha hefsaydim v'ato bachutz, which being translated means Three strikes and you are out, so God was stuck with the Universe.
So the Spirit of God moved through the heaven and on the earth and commanded that the extra dimensions should curl up on themselves, and become compact. And God looked upon it, and saw that while it was not actually good, it was better than it might have been, because at least he had light.
The First book of Moses, called Genesis, (erratum)