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Lectures

Table of Contents

Astro 100

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Cosmology and the Big Bang

Outline

1. The Expanding Universe, Revisited
2. What the Expansion Implies: a Hot Big Bang!
3. Other Evidence for the Big Bang

Terms to Know

1. The Expanding Universe, Revisited

Remember that this does NOT mean that we are at the center of the expansion! There is no center -- every galaxy sees the same redshift-distance relation and would see itself as the center of the expansion.

2. What the Expansion Implies: a Hot Big Bang!

This is what the expansion of the Universe implies: that the Universe as we know it popped into existence via a collossal, hot, dense, "event" about 15 billion years ago, and has been coasting apart ever since.

Q: Where was the center of the Big Bang?

A: There was no center! It happened everywhere at once at the same time. Space itself was created and started expanding in the Big Bang. You could just as well ask, "Where is the center of the surface of an expanding balloon?" The volume has a center, but the surface doesn't.

Be careful: we are at the center of the visible Universe (visible to us), because everywhere we look we see galaxies rushing away from us, and younger and younger galaxies farther and farther away. But this is exactly what would happen if the Universe were uniform, infinite, and expanding -- and every observer would see the same thing.

The Cosmological Principle -- which astronomers assume to be correct -- states that all observers in the Universe see the same thing. (This is true only on large scales -- not on the size of people, or planets, or stars, or galaxies, or even clusters of galaxies, but rather on sizes where the Hubble expansion looks smooth and uniform, larger than 10 Mpc or so.) There is no special, preferred place in the Universe. This is the ultimate form of the Copernican Principle.

If the Cosmological Principle is true, then the Universe should be isotropic on those large scales. This means "looks the same in all directions," and to a very high level of precision, the Universe does indeed appear to be isotropic.

3. Other Evidence for the Big Bang

1. All the light elements in the Universe (75% H, 23% He, and trace amounts of Be, Li, B, D) appear in just the relative abundances predicted by the Big Bang theory. During the first few minutes of the Universe, when there was nothing but a hot soup of particles, some recipe of nucleosynthesis cooked the particles together, banging this many protons into that many neutrons, until things cooled enough to stop the processes. The products of that recipe are the elements that make up most of the Universe. No theory besides the Big Bang has properly accounted for the observed elemental abundances.
2. We still see the afterglow of the Big Bang. For the first 0.1 million years after the Big Bang, the Universe was so hot and dense that photons would bounce off of matter before they got very far. About 100,000 years after the Big Bang, well after atomic nuclei had been formed, the expanding Universe finally cooled enough for those nuclei to capture electrons and form neutral atoms of hydrogen. This is called recombination (although it should really be called "combination," since the atoms were never combined to begin with). At that point, photons were suddenly able to fly free: the Universe became transparent.

   As we look far away and back in time towards the Big Bang, then, 15 billion light years away, we can see only so far as the time of recombination, 100,000 years after the Big Bang, since the Universe is opaque beyond (earlier than) that point. It looks like a glowing wall that hides the very early Universe from our view -- like the edge of a cloud that surrounds us almost 15 billions light years away. This is called the last scattering surface , the last time in the Universe when photons were scattered by matter. The wall is glowing with a black body spectrum of 2.73 K, so it peaks at about _peak = 1 mm, in the microwave part of the electromagnetic spectrum. This is called the cosmic microwave background (CMB), and its discovery in the 1960's garnered the Nobel Prize in Physics for Arno Penzias and Robert Wilson.

QUESTION: The last scattering surface had a temperature of about 3000 K, so why doesn't it appear like a black body with _peak = .001 mm, just beyond the visible part of the spectrum?

ANSWER: Because the photons from the CMB are redshifted 1000 times by the expansion of the Universe!

No cosmological theory besides the Big Bang has been able to account properly for the CMB.

Outline

1. Using the Expansion to Measure the Age of the Universe
2. The Fate of the Universe: Crunch or Coast?

Terms to Know

1. Using the Expansion to Measure the Age of the Universe

We can find out by "running the movie backwards" again to see how long the expansion has been taking place.

ROUGH ESTIMATE: If H = 75 km/s/Mpc, then a galaxy 100 Mpc away is receding from the Milky Way at 7500 km/s. We can use the standard distance = speed x time equation ( D = V x T, e.g., 6 km/h x 2 hours = 12 km) to find T, the age of the Universe:

T = distance / speed = 100 Mpc / 7500 km/s = 100 x 10⁶ pc/Mpc x (3 x 10¹³ km/pc) / 7500 km/s = 4 x 10¹⁷ seconds = 1.3 x 10¹⁰ years, about 13 billion years. This is called a Hubble Time, the age of the Universe determined directly from the rate of expansion.

Is the Hubble Time consistent with the ages of stars according to our understanding of stellar evolution? Just barely! The oldest globular clusters are evidently about 14 billion years old, and the age of the Universe seems to be about 14 billions years old -- but maybe just a little bit less! How can this be? We must have made some mistakes in calculating one age or the other...this is a big question in astrophysics.

Now you can see why it is so important to measure the value of the Hubble Constant!

2. The Fate of the Universe: Crunch or Coast?

Is there enough mass and therefore gravity to turn around the expansion, bringing all matter crashing back together in a gigantic "Big Crunch"? Or is there enough momentum from the expansion to overcome gravity and maintain the expansion forever?

This is one of the biggest questions in astronomy today, and many researchers have devoted their careers to finding the answer. It may be that within just the next few years we will know for sure, so stay tuned!

There are three basic possibilities:

1. Universe not dense and massive enough to halt expansion: open Universe
2. Universe has critical density: expansion slows, slows, slows, but never stops: flat Universe
3. density is high enough to halt expansion and turn it around to make a Big Crunch: closed Universe; could repeat indefinitely!

Today, the critical density is 4 x 10^-30 grams/cm³ -- about 6 H atoms per cubic meter, or 1 Milky Way galaxy per Mpc³. If we add up all the mass in stars, galaxies, dust, gas, and dark matter we can detect in the Universe, we get only about 10% of that -- so it looks at this point as if the Universe is open, and will expand forever.

In fact, there is some recent evidence that the expansion is actually speeding up, due perhaps to "extra energy" that exists even in apparently empty space. The jury is still out -- stay tuned!

Lectures

Table of Contents

Astro 100