Understanding the Expansion of the Universe and Hubble's Law

Expansion of Universe Universe Expansion In 1924, Edwin Hubble measured the period of Cepheids in Andromeda. The distance that he came up with put the object much further away than the edge of our galaxy. The only conclusion was that there are other galaxies. This was a huge fundamental shift in our understanding. As soon as Hubble realized that these spiral nebulae were external galaxies, Hubble began measuring the distances to these objects. Another bit of information that he had was their radial velocity (how fast they are moving away from us). It turned out that nearly all of these galaxies are moving away from us and, more than that, in 1929 Hubble presented one of the most important astronomical discoveries of our times: The HUBBLE LAW. The Hubble Law states that the galaxies distance is directly related to the galaxies velocity. In other words, the more distant the galaxy was, the faster it is moving away from us. This means that the universe is expanding. Hubble's Law is written as velocity = Hubble's Constant times the distance. Below is Hubble's original plot: The actual value Hubble's constant is extremely important and this was one of the main missions of the Hubble Space Telescope. The value is known now to about 5% accuracy, whereas before HST it was known to about 50% accuracy. Velocity = H0 x Distance (H0 is called Hubble's constant and it is somewhere around 70). For this equation, we put velocity in km/s and distance in Mpc. https://utexas.instructure.com/courses/1367374/pages/expansion-of-universe 1/7 10/19/23, 12:30 PM Expansion of Universe: Fa23 - POP ASTRO NONSCIENCE STDNTS (48260)

As well as Cepheids, supernova can act as standard candles. The advantage with supernovas is that they are extremely bright and we can see them to far distances. In fact, supernovas are one of our best measurements of the shape of the universe since we can see them so far back in time. Expansion of the Universe Hubble showed that the universe is expanding and this has significant consequences. First, it says that early in the universe galaxies were closer together. Extrapolating this, we realize that the universe began at an infinite density or a singularity. This eventually was formulated as the Big Bang. Another consequence is that since space is expanding, then distances between all galaxies is expanding. In other words, the universal expansion is seen by every galaxy. If the universe had been expanding since the beginning of the universe, then we can use the expansion rate (Hubble's constant) as a measure of the age of the universe. This places the age around 14 billion years. Fortunately, the age of the oldest globular cluster is around the same age (if it was older we would be in trouble). Thus, the fact that the universe is expanding confuses the issue of galaxy velocities. The question is whether the galaxies themselves are moving that fast or are they standing still and space is expanding. This expansion of space mimicking as a velocity is what we can the COSMOLOGICAL REDSHIFT. The wavelength of the emitted light is redshifted, but that can be due to either a velocity or a expansion. Latest Controversy on Hubble's Constant A. Riess (Nature Review) has recently summarized the state of the H0 differences, and there appears to be an important issue that we don't understand yet. Below are the individual measurements and the comparison:

Basic Structure In order for us to understand galaxy formation we must first measure basic properties of the Universe, for example: age, size, mass. There are three underlying principles that govern much of our understanding of the Universe. These are 1) cosmological constant, 2) the Heisenberg Uncertainty Principle, and 3) the Anthropic Principle. Dark Energy The cosmological constant was invented by Einstein. Based on his GR equations, he discovered that the Universe could not be standing still since the mutual gravitational attraction would cause it to collapse in on itself. However, he firmly believed in a static Universe (unchanging). Thus, he proposed a repulsive force that counteracted gravity. He simply inserted a fudge factor into his equations, and this was called the cosmological constant. Einstein proposed this in 1915. In 1924, Hubble discovered that Andromeda was a galaxy significantly far away from us (this was a fundamental breakthrough), and subsequently measured HUBBLE'S LAW. This results instantly showed that the Universe was expanding. This proved to Einstein that we don't live in a static Universe and that there was no need at all to include his fudge factor. Einstein calls this his biggest blunder. https://utexas.instructure.com/courses/1367374/pages/expansion-of-universe 3/7 10/19/23, 12:30 PM Expansion of Universe: Fa23 - POP ASTRO NONSCIENCE STDNTS (48260)

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Essentially noone thought that a cosmological constant existed for about 80 years after Einstein came up with the idea. Now it looks like the cosmological constant is the dominant source in the Universe! Einstein's blunder may be one of his greatest triumphs. Recent Supernova Results As we discussed earlier, the best way to understand the expansion of the Universe is to measure distances between objects. Supernovae are one of our best examples we have in order to do this. Below are a few examples of supernovae in distant galaxies. https://utexas.instructure.com/courses/1367374/pages/expansion-of-universe 4/7 10/19/23, 12:30 PM Expansion of Universe: Fa23 - POP ASTRO NONSCIENCE STDNTS (48260)

However, to use SN, we must be able to calibrate them as a standard candle. One issue is that we do not have a theoretical model for their luminosity so we have to use empirical calibrations that are based on objects that we do understand. Furthermore, not only do we need to assume we can calibrate SN, we also need to understand whether the calibration might change over time. There are multiple groups working on this project and the plot below shows the results from the two main ones. They are remarkably consistent with each other which is always a strong sign that something correct.

All of the results suggest that the Universe is dominated by the cosmological constant. Today, the cosmological constant is over twice as important as the matter in the

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Universe. This represents a huge step in understanding the structure of the Universe. The supernovae at high redshifts are very important. Just the one SN at z=1.7 was critical for a lot of the dark energy discussion: it is so distant that it puts tight constraints on the various models. However, there is still a very large uncertainty since we have to make sure we understand how supernovae evolve, if they do at all. Below is the most recent update of the SN data: Notes class 10/24 - Expansion of universe - candle: o object with known luminosity (total brightness) o measure how bright it appears o take ratio of two first points = distance  in order to get the distance you need it the light to be distributed isotopically and it needs to be a standard candle

- Isotopy: o Virtual particles and Spacetime are distributed isotopically. o - CMB - - What is Ho and what is it good for and used for? Used to relate distance of galaxies to velocities. - Hubble’s constant: V = Ho D - To get velocity you use spectroscopy. To get distance you measure what you see - How would you modify the standard candles in the near universe to match hubble’s law in the distant universe? - If the luminosity of nearby starts is brighter than what we think, how does that affect Ho? o If its brighter than we think it is, then the object would be further away. If the distance is bigger, Ho is smaller. - Hubble bubble: o We live in a bubble and there a lot of density on the outside, so all the galaxies at the edge are being pulled out because of the extra density pulling them from us.

Supernova: SUPERNOVA: massive star - Very bright - Calibrate total brightness. - = distance What stops the sun from collapsing? hydrogen burns into helium that creates high energy particles that balances out the composition of the sun. Supernova: when the nuclear star’s mass reaches 1.4, it becomes a solid surface. Material clings to it and then blows up. From supernova explosion we can get the standard candle to get the distance. Then use spectroscopy to get velocity and then we can measure the expansion of the universe. With a supernova you can measure much more. Supernovas can go wrong if light is not equally distributed over the surface area of sphere. Also, Maybe the 1.4 might vary in each supernova.

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Supernovas are the objects that told us that the universe is expanding. When we measure them, we realized: Supernovas are fainter than we expected. That means they are further away and hence the universe is expanding continually. W= density If you increase the size of the room, the volume will increase as well. Matter will change by just the volume. Radiation: when the universe expands, matter is not affected. Particles won’t change. But the density of the photons increases. Universe expands= volume increases, density increases. Wavelengths of photons stretch out. Universe expansion rate depends on: -radiation - matter Does the matter increase or decrease as we go to the past: In the past things are closer together, higher density. Density decreases with time. Problem: Dark energy has taken over matter.

Expansion of Universe

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