8.2-4

Question 1

Cosmological Principle

Answer 1

Space is homogeneous and isotropic, indicated by galaxy distribution and the 3-K cosmic micro-wave background (CMB).

Question 2

Newtonian Gravity in Cosmology

Answer 2

Newtonian theory of gravity cannot fully describe the universe, requiring general relativity for an accurate description.

Question 3

Simplification: Newtonian Cosmology

Answer 3

Important cosmological equations from Newtonian mechanics agree with general relativity, offering a simplified description of cosmology.

Question 4

Conceptual Differences (Newtonian vs Relativistic)

Answer 4

• Newtonian cosmology:
  – central universe position
  – redshift due to Doppler effect
• Relativistic cosmology:
  – expanding space
  – all points equivalent

Question 5

Newtonian Cosmology Principles

Answer 5

Adopts two principles from general relativity:
A) Validity of special relativity
B) Einstein’s equivalence principle

Question 6

The Metric in General Relativity

Answer 6

• Metric describes the curvature of spacetime
• Geodesics represent the shortest path between two points in this space

Question 7

Examples of Curvature

Answer 7

• Flat surfaces have straight line geodesics
• Curved surfaces have curved geodesics

-> Sum of angles in triangles differs based on curvature

Question 8

Metric Description

Answer 8

Metric describes the squared distance between nearby points, varying based on the presence of gravitational fields.

Question 9

Metric for the Universe

Answer 9

Based on the cosmological principle, the universe’s metric has uniform curvature, leading to three geometries:
- flat
- spherical
- saddle-like

Question 10

3-Dimensional Space Metrics

Answer 10

Different formulations of metrics for 3-dimensional space suggest various geometries and curvature types.

Question 11

Volume of a Positive Curved Universe

Answer 11

Positive curved space has a finite volume, calculated using specific metrics and integral formulas.

Question 12

Spacetime

Answer 12

Incorporates time according to special relativity, leading to the Robertson-Walker metric for 4-dimensional spacetime.

Question 13

An Expanding Universe

Answer 13

Describes the universe’s expansion in terms of:
- co-moving coordinates
- distance
- expansion speed

relating to the Hubble law

I find this a bit random hahah, or at least one would have to find a better front side of the card