Quick questions on Origins of the elements and the Big Bang: HSC Physics Module 8

Edwin Hubble (1929) measured distances to galaxies using Cepheid variable stars and found that the redshifts of their spectra (taken to be Doppler shifts of recession) were proportional to those distances:

Penzias and Wilson (1964) discovered an isotropic microwave hiss in their antenna that could not be attributed to instrument noise or known sources. The spectrum measured precisely by the COBE satellite (1989) is the most perfect blackbody known in nature, with $T = 2.725$ K.

Between about 1 second and 3 minutes after the Big Bang, the universe was at a temperature comparable to nuclear binding energies. Free protons and neutrons combined to form light nuclei:

The Big Bang model does not describe "what came before"; it describes the evolution of the universe from a hot dense state of which we have direct evidence (the CMB and primordial element abundances).

A galaxy shows the H$\alpha$ line at 670 nm instead of its rest wavelength 656.3 nm. Estimate the recession velocity and the distance to the galaxy, using $H_0 = 70$ km/s/Mpc.

It was an expansion of space. There is no centre and no edge; every observer sees galaxies receding from them in all directions.

$H_0$ has units of 1/time. The product $H_0 d$ has units of velocity.

The CMB photons we observe come from the recombination epoch, when the universe was 380000 years old, not from the Big Bang itself. Earlier light cannot reach us because the universe was opaque.

Only the lightest elements (mainly H and He, traces of Li) come from primordial nucleosynthesis. Carbon, oxygen, iron and everything heavier require stars and supernovae.

$1/H_0$ assumes a constant expansion rate. The actual age (13.8 billion years) accounts for varying expansion under gravity and dark energy, but $1/H_0$ is close enough for HSC estimates.