Derive, using the concept of the cosmological origin of redshift, the relation

T \( \propto \frac{1}{R}\)

between the temperature T of the cosmic microwave background (CMB) radiation and the cosmic scale factor R.

The present temperature of the CMB is 2.8 K. This radiation was emitted when the universe was smaller by a factor of 1100. Estimate the temperature of the CMB at the time of its emission.

State how the anisotropies in the CMB distribution are interpreted.

the cosmological origin of redshift implies that the wavelength is proportional to the scale factor: \(\lambda \) \( \propto \) R

combining this with Wien’s law \(\lambda \) \( \propto \) \(\frac{1}{T}\)

OR

use of kT \( \propto \frac{{hc}}{\lambda }\)

«gives the result»

Evidence of correct algebra is needed as relationship T = \(\frac{k}{R}\) is given.

[2 marks]

use of T \( \propto \)\(\frac{1}{R}\)

= 2.8 x 1100 x 3080 ≈ 3100 «K»

[2 marks]

CMB anisotropies are related to fluctuations in density which are the cause for the formation of structures/nebulae/stars/galaxies

OWTTE

[1 mark]