Cosmology | Lecture 3 | Summary and Q&A

Transcript

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Summary

This video discusses the basic equations of cosmology, including the Friedman Robertson Walker equation and its connection to Einstein's equations. It explains the concepts of matter-dominated and radiation-dominated universes and how the energy density and temperature change with the scale factor of the universe.

Questions & Answers

Q: What are the basic equations of cosmology?

The basic equations of cosmology include the Friedman Robertson Walker (FRW) equation and Einstein's equations.

Q: What is the Friedman Robertson Walker equation derived from?

The Friedman Robertson Walker equation is derived from energy conservation, assuming homogeneity of the universe.

Q: How does the universe look on scales larger than clusters of galaxies?

On scales larger than clusters of galaxies, the universe appears to be homogeneous and smooth.

Q: What is the basic equation of cosmology?

The basic equation of cosmology is the Friedman Robertson Walker (FRW) equation.

Q: How can the FRW equation be written in a more familiar form?

The FRW equation can be written as the square of the Hubble constant times the energy density equals a constant minus the curvature divided by the scale factor squared.

Q: What is the connection between the FRW equation and Einstein's equations?

The FRW equation is essentially the time component of Einstein's equations, describing the curvature of space and the energy-momentum tensor of the universe.

Q: What does it mean for the universe to be matter-dominated?

A matter-dominated universe is one where the energy is mainly in the form of particles at rest, such as galaxies, protons, and neutrons.

Q: How does the energy density of matter change as the universe expands?

As the universe expands, the energy density of matter decreases as one over the scale factor cubed.

Q: What is the equation for the expansion of a matter-dominated universe?

The equation for the expansion of a matter-dominated universe is a dot over a squared equals 8 pi G over 3 times the energy density of matter minus the curvature divided by the scale factor squared.

Q: What is the power law solution for the expansion of the universe?

The power law solution for a matter-dominated universe is that the scale factor grows as a constant times time to the two-thirds power.

Q: How does the universe transition from being radiation-dominated to being matter-dominated?

The universe transitions from being radiation-dominated to being matter-dominated when the energy density of matter becomes larger than the energy density of radiation.