5.3 The redshift of the 3 K radiation
The temperature, T, of the radiation is proportional to the most probable photon energy, E, which as we have said is proportional to f, and hence inversely proportional to the wavelength λ. Thus,
According to Equation 1, we have for the redshift, z
The wavelength we observe now, λ0, is that corresponding to T ≈ 3 K, whereas the original wavelength, λ1, emitted during the decoupling epoch corresponded to T ≈ 3000 K. Hence
and hence z ≈ 1000. This compares with z ≈ 6 for the furthest optical object so far seen (2004). This was associated with a quasar.
Quasars are believed to be the highly luminous centres of certain galaxies at an early stage in their life. They can be 1000 times brighter than a typical galaxy and can therefore be seen at great distances.
From these z values, you can appreciate how much further back in time and farther away in distance it is possible to look with a microwave detector than with an optical telescope. Even so, it is important to recognise that we cannot, and never shall be able to, see right back to the instant of the big bang. For the first 4 × 105 years, the Universe was opaque.
The wavelengths associated with photons increase as t2/3, where t is the time they were emitted after the big bang. Assuming the time now, t0 = 1.4 × 1010 years, and that decoupling took place when T = 3000 K, estimate the time, td, at which decoupling occurred.