Cosmology

Olber’s-paradox

parsec = 3.26156 ly

• this is the hypothetical distance at which a star would show parallax of exactly one second

Assumptions in cosmology:

1. when averaged over sufficiently large scales, the observable properties of the universe are isotropic (independent of direction)
   • nearby galaxies are anisotropically distributed, distant galaxies approach isotropy, the cosmic microwave background is almost perfectly isotropic
2. cosmological principle = our position in the universe is not preferred to any other. Combining these two points means that the universe is both homogenous and isotropic

Redshift (z) = the difference in observed wavelength and emitted wavelength of light

• due to the expansion of space

To understand what universe we live in, we need to determine observationally the following numbers:

1. The Hubble parameter $H_0$
   • requires distant measurements
2. The current density parameter ${\text{ohm}}_0$
   • requires mass density measurements
3. The cosmological constant $\Lambda$
   • requires acceleration measurements
4. The age if the universe $t_0$
   • requires age measurements

Friedmann’s equations

• At cosmological scales, other interactions than gravity are unimportant.
• The cosmological standard model assumes general relativity as the appropriate theory of gravity.
• General relativity is a metric theory of gravity, describing gravity as a geometric effect on the metric of space-time.
• According to general relativity:
  • space is 4 dimensional
  • matter (=energy) modifies space (Einstein Field equations)
  • At each point, space is locally Minkowski