World Science Scholars
1.2 The Expanding Universe
summary
In the last two decades, astrophysicists & cosmologists have made incredible discoveries.

• One of the most paradigm-shifting discoveries was when observations of exploding stars called supernovae revealed that we live in a universe which is not only expanding, but is accelerating.
• This acceleration is propelled by a new mysterious element of the universe that we call dark energy, but about which we know very little.
• How did we view the universe before this discovery? We already knew the universe was expanding and chock-full of billions of galaxies. The Hubble Deep Field image exposed thousands and thousands of galaxies in an incredibly small patch that appeared dark previously.
• When we look at an image like the Hubble Deep Field, it would seem that our universe is static—the shutter was left open for a very long time and yet nothing is blurry. But ever since the Big Bang, the separation between galaxies has been growing, and the further away a galaxy is from us, the faster it appears to be moving away.

How do we really know the universe is expanding?

• The best confirmation would be to observe galaxies actually moving away from us. In order to do so, we have to first tackle to problem of figuring out galactic distances.
• One method of doing so is the method of parallax. Parallax uses the apparent motion of distant stars against an even more distant background, as our observation angle changes during our orbit about the Sun. Using simple geometry can tell us a star’s distance based on the apparent angle change, but after a certain distance this method becomes inaccurate due to the angles becoming so small.
• Another method we can use is to observe the brightness of a known object. The further away it is, the dimmer it should appear, just as a ship’s captain can judge his distance from shore-based on the brightness of a nearby lighthouse.
• Of course, intermediate dust (or fog, in the ship captain’s scenario) could trick us into believing the object is farther away than its brightness would suggest.

Standard candles help determine galactic distances.

• For making these measurements in space, we have to rely on telescopes and whatever nature provides. It turns out nature provides something that is quite similar to a lighthouse, a star we refer to as a standard candle, because we understand its luminosity so well that it makes an excellent reference point.
• A galaxy might contain some hundred billion stars, and about once every hundred years, a single star may explode in that galaxy, known as a supernova. These are extremely luminous—billions of times brighter than our sun—and by observing its brightness we can gauge how far away it is.
• We can do this in a very quantitative way, because we know that light will obey the inverse square law.$$\text{Brightness} \propto \frac{1}{r^2}$$In other words, a star twice as far will appear four times dimmer; a star three times as far will appear nine times dimmer. You can imagine this as the light having to “paint” the surface of a larger and larger sphere centered on us.
• The other requirement is to measure the apparent motion of galaxies away from us. Light is emitted by objects in the universe at generally known wavelengths of light that we can determine in the laboratory—but as it propagates through an expanding universe, space stretches and we receive a red-shifted, or longer wavelength, light. We can measure that redshift.
• This might remind of the Doppler shift, but there is a key difference: it’s not that the distant object is really moving away from us at that rate, it’s that space itself is expanding. If it were an object that were just moving away from us, we would have no reason to believe that any other object nearby would have any predictable motion. If it’s space that’s expanding, however, then we have a predictable pattern.

What does the evidence show?

• We can pick out individual galaxies that have these supernovae in them, and we can measure their distance and apparent motion away from us. The linear relationship that these two variables have is the signature mark of an expanding universe. And this isn’t just a thought experiment: this relationship was first demonstrated by astronomer Edwin Hubble, who combined measurements of redshifts from Vesto Slipher with his own measurements of galactic distances.
• The measured slope of the line, $$H_0=\frac{v}{d}$$gives the expansion rate of the universe today, where $H_0$ is known as Hubble’s constant. The fact that it was a positive slope implied our universe was expanding.
• We can now immediately address a deep, philosophical question: When did the universe begin? Hubble’s Law tells us how fast the universe is expanding, so the inverse of the Hubble constant $H_0$ will give us the approximate age of the universe, if no forces are acting on the universe to change the rate. From Hubble’s initial value of $H_0 = 500 \ \text{km/s/Mpc}$, we get that the age of the universe is $\frac{1}{H_0}\approx$ 2 billion years old.
• But this number was immediately recognized as incorrect. In 1929, we knew that even the Earth was older than that, but over the next 80 years, our measurement tools improved, and we’ve learned that the universe is really 13.82 billion years old.

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