Launchpad Day 5: Cosmology (Mike Brotherton)

Hubble’s Law

When we measure the distances to galaxies and their velocities, we find out that they are correlated. We take the spectrum of the galaxy and can tell distance. But because of the geometry of space/time things that are far away do not always look smaller.

We can model what’s happening in the Hubble’s Law by imagining a block of space. Space expands carrying the galaxies along with it. The galaxies themselves are not expanding. On large scales, galaxies are moving apart, with velocity proportional to distance. It’s not galaxies moving through space. You will measure the same Hubble’s Law no matter which galaxy you are in. The velocity is proportional to the distance. The ones farther away appear to be expanding faster.

You can take an overlly simple version of the Hubble’s Law and try to run it backwards to see when everything was together. Time = distance/velocity

Velocity = (Hubble constant) * distance.

T ~~ d/v = 1/h ~ 14 billion years.

The more distant the objects we observe, the further back into the past of the universe we are looking. As we look further away, we are looking back in time. If the universe has a finite age then we can only see to a finite distance, which does not mean that the universe has an edge. The radiation from the very early phase of the universe should still be detectable today. Black body radiation with a temperature of T = 2.73 K. It was discovered in mid-1960s as the Cosmic Microwave Background Radiation.

Wilson and Penzias wrote this innocuous paper about this noise in their system that they couldn’t get out. Cleaned out pigeon crap and other things, because they didn’t expect to see this radiation. At Princeton someone knew about the Big Bang theory. There should be a time in the universe when everything would have been like the surface of the star. But the expansion would stretch it out from a 3000 degree blackbody that would redshift to 2.73K. The team at Princeton was building a machine like Wilson’s and Penzias’s to detect the microwave background radiation, but Wilson and Penzias beat them to it by accident.

Universe cools as time passes and expands as time passes. Temperatures range from 1 degree Kelvin up to 10¹⁰ degrees Kelvin. Expanding space is completely consistent with understanding of general relativity.

First a dense ionized gas. Then low-density ionized gas. Then neutral recombined gas. It’s hard to look through a plasma like ionized gas. So it’d be like trying to look through the surface of a star. You can look a little way, but a star is opaque. The universe was like that. At optical wavelengths H is transparent. If you look back in time, recombination happens so we can look back through H and the universe looks like the surface of a star.

Early universe is very high energy. There are electron and positron pairs. It was a soup of particles and radiation. There was an equilibrium between particles and energy, with most of the energy being contained in radiation. We go from the soup of particles and radiation to a time when particles are able to remain stable. That is a high energy gamma-ray photon no longer exists with enough energy to blow them apart. We have both protons and neutrons in the universe. Proton and neutrons form a few helium nuclei.

There were only a few minutes where the universe was like the heart of a star. Photons are incessantly scattered by free electrons. The early universe was opaque. We call that the radiation dominated era. Protons and electrons recombine to form atoms => Universe becomes transparent for protons. This epic of recombination happens at redshift 1000, which is a few hundred thousand years old. Be careful when talking about size. Universe was a billion times denser then.

After recombination, photons can travel freely through space.

when we look at the gas between galaxies today, the gas is ionized. Therefore there was an epic of reionization. We’ve identified it as redshifts of about 6. It started around 16 and by the time you get to 6 the whole thing is ionized.

Cosmological Principles. These may not be strictly speaking always true.

• Homogeneity: On the largest scales, the local universe has the same physical properties throughout the universe. Every region has the same physical properties

• Isotropy. On the largest scales, the local universe the same in any direction one looks.

• Universality. The laws of physics work the same everywhere.

Shape and Geometry of the Universe.

Back to our 2-dimensional analogy. How can a 2-d creature investigate the geometry of the sphere? Measure curvature of its space.

According to the theory of general relativity, gravity is caused by the curvature of space-time. The effects of gravity on the largest cosmological scales should be related to the curvature of space-time. The curvature of space-time, in turn is determined by the distribution of mass and energy.

Deceleration of the Universe

The theory says that the universe is expanding, but the gravity of the universe should be slowing it down. We can define the critical density, which is the critical density of matter, which is just enough to slow the cosmic expansion to a halt at infinity.

If it’s perfect critical case, the universe flat. If we’re going to expand for ever, it’s hyperbolic geometry. If it’s going to collapse, its curved geometry

Problems with the Classical Decelerating Universe model.

The flatness problem. The thing is, if the universe weren’t perfectly flat from the beginning, it turns out that for it to be this close to critical density today, in the past it would have to be hugely different. Extreme fine tuning required.

2. The isotropy of the cosmic microwave background.

We talked about the size of the observable universe, back when the universe was a feew hunderd thousand years old at the time of the recombination. Light has not had time to travel across the universe at the age of recombination.

The solution is that the universe is expanding faster than the speed of light. There is no speed limit on the expansion of space because nothing is actually moving. The idea is that universe is really tiny, really dense at one point and then it inflates. Grand Unified Theory. If we apply the period of sudden expansion during the early evolution of the universe the it solves the problems.

By observing type Ia supernovae, astronomers can measure the Hubble relationship at large distances and measure the deceleration.

Universe expansion is accelerating. SURPRISE! They went out to measure the deceleration and discovered that it wasn’t happening. Basically, as you look at more distant objects, more distant supernovas, they turn out to be a little more distant than we expected giving their velocities.

Cosmic acceleration can be explained with the cosmological constant. Lambda is a free parameter in Einstein’s fundatmental equation of general relativity; previously believed to be 0. Einstein didn’t think it looked like the universe was expanding, so he put this in to make correct for that in his equation. Then Hubble showed that the universe was expanding. So people set Lambda to be 0. Energy corresponding to Lamda can account for the missing mass/energy and makes everything work. We call it “Dark Matter.”

Evolution and fate of the universe.

The big empty or the big rip. Not sure which.

The big empty, things would keep traveling apart until nothing outside the galaxy would be visible.

The big rip, the curve would cause atoms to rip.

Fluctuations in the Cosmic Microwave Background.

Angular size of the CMB fluctuations allows us to probe the geometry of space-time. We can do models that relate the curvature and the spot size pattern and compare it to what we actually see and it’s very much like the flat model universe. We can analyze the frequency of signal.