Assigning a distance by redshift
The Hubble law lets us use a simple spectrum of a galaxy to figure outwhere 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”
Galaxy “Filaments”
QSO
us
Redshifts tell us where everything is…
Cosmic FoamGravity 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 DestinyThe shape depends on the curvature of spacetimeThe 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 UniverseSince 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…
A perfect blackbody (thermal) spectrum: 2.736 K
Cosmic dipole (motion)
Penzias & Wilson (and Dicke)
Minute structure then
galaxies todayThe 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 NucleosynthesisFrom 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 meters1 heavy (more than O) atom100 atoms of C,N,O100,000 atoms of helium1,000,000 atoms of hydrogen30 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 spectrumThe 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.
