Transcript Redshift takes us from 2-D to 3-D

Assigning a distance by redshift
The Hubble law lets us use a simple spectrum of a galaxy to figure out
where it is along the
line-of-sight. Higher
redshifts indeed go with
smaller and fainter
looking galaxies.
Redshift takes us from 2-D to 3-D
Huge surveys are ongoing to
get redshifts for hundreds of
thousands of galaxies. These
give us the large-scale
structure of the Universe.
Quasar Spectra and the “Lyman-alpha Forest”
Redshifts tell us where
everything is…
us
Galaxy “Filaments”
QSO
Cosmic Foam
Gravity acting on dark matter gives the basic layout of matter in space.
Clusters will continue to collect, but the space between them will
continue to expand.
Density is Destiny
The shape depends on the curvature of spacetime
The curvature of spacetime depends on density
“flat” corresponds to the “critical density”
~10-29 gm/cc beyond which the Universe
would recollapse
Curvature of the Universe
Since gravity is spacetime curvature,
the density sets the geometry. In
principle, we can measure the
geometry of spacetime through
geometrical tests. These tell us our
ultimate fate.
Spacetime Diagrams
In order to picture spacetime
(which is 4-dimensional), it
helps to get rid of some
spatial dimensions, and
keep time as a shown
dimension.
Here is a diagram with only
2 dimensions, one space and
one time. Light is the fastest
thing in it, and marks out
“lightcones” which
determine what can be seen,
and when. An object’s
existence is a “worldline”.
The Spacetime
Diagram of an
Expanding Universe
If space expands with time,
a 2-D spacetime diagram
looks like this. All spatial
points converge at the
beginning. The Universe is
opaque for a time, so you
see the fireball in the
distant past in all
directions. You see more
distant objects as they
were in the more distant
past. Beyond a horizon, the
rest is unobservable (now).
Lookback times
Conceptual Framework for the Big Bang
1) As you run the movie backwards (look back in time), the Universe shrinks and
gets hotter.
2) The average photon increases in energy with decreasing time, and the photon
density goes up like T4 (matter density like T3).
3) Energy and mass are equivalent, so they will freely exchange when
E average>mparticlec2 for a given particle.
4) The particles created from energy must be equal numbers of matter and
antimatter (to conserve all quantum numbers).
5) Once the matter froze out (going forward in time), all the antimatter would
annihilate with the matter, leaving energy (which gets redshifted down below
the threshold energy to make particles again). Since there is matter now, there
must have been a slight overproduction of matter compared with antimatter.
This tiny symmetry violation (1 per 100 million) produced all the particles
now in the Universe. You can infer that there are 100 million photons for
every proton. Where are they…?
Energy
matter +
antimatter
Energy
The Cosmic Background Radiation
Those photons should be all around, but very
cool (redshifted). And they are…
Cosmic dipole (motion)
Penzias & Wilson (and Dicke)
A perfect blackbody
(thermal) spectrum:
2.736 K
Minute structure then
 galaxies today
The fireball had to have some structure,
or we wouldn’t have any now. The
effort to find it was epic; it was only
seen at one part in 100,000.
Galactic plane
Astro Quiz
Which one of the following is NOT good evidence for a
moment of Creation for the Universe.
1) Very distant galaxies have extremely high redshifts.
2) The sky is much darker at night than during the day.
3) There is much more dark matter than luminous matter.
Observational Evidence of Creation
1) The sky is dark! (Olber’s Paradox)
If the Universe were infinite in space and time, every line of sight
would eventually end on a star. Even if it were very far away and
faint, that would be made up for by having more of them in a
smaller patch of sky. The sky should have the same brightness as
the Sun (or at least an M star!). This resolved by the fact that the
Universe started a finite amount of time ago (the expansion helps
too with the redshift).
Observational Evidence of Creation
2) The Universe is observed to be expanding (so in the past it was smaller).
The Steady State Universe tried to get around this by supposing that new
galaxies appear out of nowhere to fill the increasing volume
(no more unreasonable than supposing that the Universe appeared).
But then the past shouldn’t look different than the present (on average)
3) The Universe was hot and opaque in the distant past.
This is proven by the thermal cosmic background radiation. Only if all
space were opaque would all space be filled with thermal photons (and their current
temperature is reasonable given the expansion factor)
4) A theory which supposes the Universe evolves in this way can predict how the
composition of the Universe arose from the primordial fireball. These predictions are
borne out well by the current observed composition.
It seems inescapable that the Universe is only 10-20 billion years old,
and that it started at a set and knowable point of time.
The moment of Creation is now an empirical fact.
Big Bang Nucleosynthesis
From t=1-200 sec the Universe had about the density of water and a temperature
of about a billion degrees. Protons and neutrons froze out of the radiation field
(fewer neutrons because they are a little more massive), and neutrons began to
decay. There were 14 protons for 2 neutrons. The neutrons fused to make
deuterium, and then helium. This left 12 protons and 1 helium (He4), or about 8%
He by number or 25% helium by mass. Just as we see everywhere today! A little
bit of deuterium and lithium was also left, and we see that too. The exact density
then determines the amount left today (so we know what it was).
Density and Composition of the Universe
Based on what we can see, stars fall short of providing the critical
density by a factor of 200. Neutrinos don’t seem to help. Indeed, the
fraction of helium observed implies that matter is a factor of 20 short.
But there are good theoretical reasons to believe the curvature is flat.
Dark matter provides about a third of what is needed.
What’s in the Universe:
VACUUM
Counting particles in 100 sq meters
1 heavy (more than O) atom
100 atoms of C,N,O
100,000 atoms of helium
1,000,000 atoms of hydrogen
30 times that mass in dark matter
(particles of unknown mass)?
100,000,000,000,000 cosmic photons
and as many cosmic neutrinos
A Brief History of Time
Determining the geometry (fate) of the Universe
CMB Anisotropy spectrum
The details of the features on
the fireball (CMB) tell us
what the curvature of
spacetime is. They confirm
that it is flat, which means
the Universe will not
recollapse, but will expand
forever.