Cosmology | Lecture 4 | Summary and Q&A

Transcript

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Summary

In this video, the professor answers questions about the apparent wavelength of cosmic radiation, the isotropy of photons, the Doppler effect, and the relationship between relative velocity and the speed of light. He also discusses the expansion of space and its effect on light rays, as well as the different components of energy density in the universe.

Questions & Answers

Q: Does the apparent wavelength of cosmic radiation depend on the motion of the observer? Is there a Doppler effect? Is there a preferred frame of reference?

Yes, the apparent wavelength of cosmic radiation does depend on the motion of the observer, resulting in a Doppler effect. If an observer is moving through space, they will see photons from different directions with different wavelengths. This creates a bias in the sky where some directions will have hotter, higher energy photons, while others will have lower energy photons. However, there is a preferred frame of reference where the cosmic microwave background appears isotropic from all directions. This preferred frame of reference is the same as the one defined by the galaxies themselves.

Q: What is the isotropy of photons? How is it related to the temperature of the cosmic microwave background?

Isotropy refers to the fact that photons coming from different directions in space have similar energies. In the context of the cosmic microwave background, this means that the temperature of the photons is well described by their average energy. In intergalactic space, far away from the Sun and other stars, the cosmic microwave background appears isotropic, meaning photons come at you from every direction with approximately the same energy.

Q: How does the expansion of space affect light rays? Is there a limit to the relative velocity between two galaxies?

The expansion of space causes the wavelengths of light rays to stretch, resulting in a redshift. As space expands, the distance between objects (like galaxies) also increases, causing the recession velocity between them to exceed the speed of light. In a flat space, there is no bound on the distance that can be reached, allowing for relative velocities greater than the speed of light. However, this does not violate Einstein's theory of relativity because these distant objects cannot send signals faster than light back to an observer.

Q: Does the addition of velocities formula hold in relativity? Can the relative velocity between two galaxies exceed the speed of light?

The ordinary formula for the addition of velocities does not hold in relativity when it comes to the speed of light. If two observers pass each other and measure each other's velocities, the combined relative velocity may appear greater than the speed of light. However, this does not violate relativity because distant objects moving away faster than the speed of light cannot send signals faster than light back to an observer. The limitation applies to objects passing each other at extremely close distances.

Q: How does pressure relate to energy density in radiation-dominated universes?

In a radiation-dominated universe, the pressure is equal to the energy density divided by three. This relationship holds because not all photons contribute equally to the pressure in all directions. On average, one-third of the photons contribute to the pressure in each direction.

Q: Is there a relationship between the relative velocity exceeding the speed of light and the surface of last scattering? Does the size of the observable universe depend on this?

In a universe where the relative velocity between objects exceeds the speed of light, there is a distance beyond which objects are moving away too fast to send signals back to an observer. This distance is known as the cosmic horizon and defines the size of the observable universe. The surface of last scattering, which is slightly closer to an observer, is where light waves are infinitely stretched due to the expansion of space.

Q: Does the wavelength of light from the surface of last scattering decrease as the scale factor gets larger?

The wavelength of light from the surface of last scattering does not decrease as the scale factor gets larger. Instead, the wavelength is infinitely stretched due to the expansion of space. This effect is known as the Doppler shift or cosmological redshift. While the expansion of space itself causes the stretching of wavelengths, it can also be thought of as a result of the expansion of the universe.

Q: What is responsible for the expansion of space and the increase in the size of the observable universe?

The expansion of space is attributed to the properties of space itself, not specific atoms or objects moving in space. Space is constantly filling in with newly formed space, resulting in an exponential growth of the size of the universe. This expansion is described by the equations of general relativity and the expanding metric of space-time.

Q: Is the expansion of space similar to stretching a rubber band?

No, the expansion of space is not similar to stretching a rubber band. When a rubber band stretches, it thins out and decreases in mass density. In contrast, as space expands, it does not thin out, and there is no change in the mass density. The expansion of space is more accurately described as the addition of new space through the equations of general relativity.

Q: How does the expansion of space affect distant objects and the cosmic horizon?

As space expands, distant objects will eventually move beyond the cosmic horizon and become invisible to an observer. The cosmic horizon is the distance beyond which objects are moving away faster than the speed of light, preventing any signals from reaching an observer. However, nearby objects and those gravitationally bound to us, like the solar system and our galaxy, will not be affected by the expansion and will remain observable.