# Cosmology | Lecture 2 | Summary and Q&A

## Summary

This video discusses the dynamics of cosmology, focusing on the evolution equations that govern how the universe expands or contracts over time. The speaker explores the concept of flat space and how it can be curved when the space itself is expanding or contracting. The video also delves into the measurement of distances in expanding space and the relationship between the expansion and the forces holding objects together. The speaker then introduces the metric of space-time and discusses its time dependence. Finally, the video touches upon Newtonian cosmology and the behavior of particles in a gravitational field.

## Questions & Answers

### Q: What are the dynamics of cosmology?

The dynamics of cosmology refers to how the scale factor, which represents the distance between neighboring points in space, changes over time. It encompasses understanding how the universe grows, shrinks, or evolves and the equations that govern these changes.

### Q: What are the Friedman-Robertson-Walker equations?

The Friedman-Robertson-Walker (FRW) equations are the evolution equations that determine how the scale factor changes with time in an expanding or contracting universe. They describe the dynamics of cosmology from a cosmological perspective.

### Q: How is the expansion of the universe related to the Hubble constant?

The expansion of the universe is related to the Hubble constant. Hubble's law states that the velocity of a galaxy is proportional to its distance from us. The Hubble constant represents the proportionality constant in this relationship. However, the Hubble constant is not constant with respect to position and time, as it varies with time in an expanding universe.

### Q: Can space be flat while space-time is curved?

Yes, it is possible for three-dimensional space to be flat while space-time is curved. This occurs when the metric describing the flat spatial slices in four-dimensional space-time is time-dependent and the space itself is expanding or contracting. In this scenario, the space-time itself is curved.

### Q: Do measuring rods expand in an expanding universe?

No, measuring rods do not expand in an expanding universe. The forces holding meter sticks together, such as electrical and magnetic forces, are much stronger than the forces due to expansion. Therefore, meter sticks are not affected by the ambient expansion of the universe. However, large and diffuse objects like galaxies, which do not experience strong gravitational forces, will expand with the expansion of the universe.

### Q: How can the expansion of the universe be modeled as a force between points?

The expansion of the universe cannot be directly modeled as a force between points. While expansion by itself does not create a force, some types of expansion, such as accelerated expansion, can be modeled as a force between points. However, the forces due to expansion are much smaller than the interatomic forces holding objects together and cannot be measured in terms of the slight modification of the size of a meter stick.

### Q: Is the Hubble constant constant with respect to position in space?

Yes, the Hubble constant is constant with respect to position in space. It does not vary from point to point, which is a property of homogeneity. However, the Hubble constant is not constant with respect to position and time, as it varies with time in most scenarios.

### Q: How does the metric of space change with the expansion of the universe?

The metric of space changes with the expansion of the universe by a factor called the scale factor. This scale factor represents the distance between neighboring points at a fixed instant of time. As time progresses, the scale factor determines how the actual distance between these points grows or shrinks. In an expanding universe, the scale factor increases with time, leading to larger separations between objects.

### Q: What is the metric of space-time in a homogeneous and isotropic universe?

In a homogeneous and isotropic universe, the metric of space-time is time-independent and described by the Friedmann-Lemaître-Robertson-Walker (FLRW) metric. The FLRW metric has a fixed coefficient in the time-time component, while the space components are negative and proportional to the square of a function called the scale factor, which represents the distance between neighboring points.

### Q: How does energy conservation relate to the motion of particles in a gravitational field?

Energy conservation is an important concept when studying the motion of particles in a gravitational field. The total energy, including kinetic and potential energy, of a particle remains constant over time. This means that the sum of the kinetic and potential energy, which depend on the mass, velocity, and distance, remains the same for a given particle. This allows us to understand how particles behave under the influence of gravity and determine their escape velocities or bound orbits.

## Takeaways

In this video, the speaker delves into the dynamics of cosmology, focusing on the scale factor and how it changes with time. They discuss the expansion of the universe, its relationship with the Hubble constant, and the behavior of objects in an expanding space. The video also touches upon the metric of space-time, proper time, and the energy conservation concept in gravitational fields. Overall, this exploration provides valuable insights into the foundations and principles behind the study of cosmology.