Cosmology Lecture 2

Transcript

stanford university let's review a little bit and then i want to move on to um generalizations of what we've talked about so far i think we worked out we worked out the equations of an expanding universe they were newton's equations let's talk about something else first does newton's equations really get it right yeah newton's equations does get it... Read More

Summary

In this video, the speaker discusses the expansion of the universe and the equations that describe it. The speaker explains the difference between Newton's equations and Einstein's equations, and introduces the concept of curved space-time. They also discuss the role of photons in the universe and how they affect the equations. Finally, the speaker introduces the Friedman equation and explores its implications for the expansion of the universe.

Questions & Answers

Q: Does Newton's equations accurately describe the expanding universe?

Newton's equations accurately describe the expanding universe for the most part. However, Einstein's equations, which take into account curved space-time, are more suitable for studying the universe as a whole.

Q: What is curved space-time and how does it affect the universe?

Curved space-time refers to the idea that space itself can be curved. This means that if you were to measure triangles or perform geometric exercises in space, you might find that it is not flat but curved. In the case of the universe, this curvature can be visualized as a three-dimensional version of a sphere. The curvature of space-time has implications for how galaxies move relative to each other and how they move apart from each other.

Q: Can Newton's equations still be used to study the local behavior of galaxies?

Yes, if the galaxies are relatively close to each other and moving slowly with respect to each other, then Newton's equations can be used to study their behavior locally. However, if the galaxies are moving with a significant fraction of the speed of light relative to each other, then Einstein's equations need to be considered.

Q: What are some of the particles in the universe that move close to the speed of light?

Neutrinos and photons are examples of particles in the universe that can move close to the speed of light. Photons, in particular, are present in the universe as radiation and can affect the equations used to study the expanding universe.

Q: How is the density of matter in the universe related to the mass contained within a given volume?

The density of matter in the universe, denoted as rho, is related to the mass contained within a given volume by dividing the mass by that volume. This relationship allows us to measure the density of matter in units such as kilograms per cubic meter.

Q: How does the scale factor of the universe, denoted as "a", affect the equations?

The scale factor, "a", is a bookkeeping device in the equations and does not have a physical meaning by itself. However, ratios of scale factors at different times are physically meaningful and can indicate the expansion or contraction of the universe.

Q: What is the Friedman equation and how does it relate to the expansion of the universe?

The Friedman equation is a key equation in cosmology that relates the expansion rate of the universe, denoted as a dot over a squared, to the density of matter, denoted as rho. It also includes a term known as c, which represents the total energy of the universe. The equation can be solved to understand how the universe expands or contracts based on different values of c and rho.

Q: How does the total energy of the universe affect the expansion?

The total energy of the universe can be positive, negative, or zero. If the energy is positive, the universe will continue to expand. If the energy is zero, the expansion will depend on the density of matter. If the energy is negative, the universe will eventually contract.

Q: How does the expansion of the universe change as a becomes very large?

When the scale factor, a, becomes very large, the expansion of the universe behaves as a straight line with constant velocity. This is a non-accelerated motion that continues indefinitely as long as the energy is positive.

Q: What happens if the energy of the universe is negative?

If the energy of the universe is negative, there is a crossover point where the expansion of the universe transitions to contraction. This occurs when the term 8πGρa³ becomes zero, indicating that the universe momentarily comes to rest before collapsing.

Takeaways

The expansion of the universe can be described by the Friedman equation, which relates the expansion rate to the density of matter and the total energy of the universe. If the energy is positive, the universe will continue to expand indefinitely. If the energy is negative, the universe will eventually contract. The behavior of the expansion depends on the values of these parameters and can be understood by studying the equations and their implications in different scenarios.