1 The visible matter in the Universe, stars and interstellar gas, is concentrated into galaxies, which are collections of ~1011 stars. The galaxies themselves are usually to be found in clusters with typically tens or hundreds of members. The clusters, in their turn, are loosely associated in superclusters.
2 Distances are estimated via a series of intercalibrated techniques, each overlapping with and extending further than the previous one. The principal stages are:
Earth–Moon and Earth–Sun distances involving radar ranging;
Triangulation to nearer stars, using the diameter of the Earth's orbit as baseline;
Calibration of luminosity against temperature for typical stars, using the stars of the Hyades cluster;
Period-luminosity relationship for Cepheids, first for stars in our Galaxy, then in other galaxies;
Type Ia supernovae, first in nearer, then in further-off galaxies; Classification of galaxies into recognisable types, of different luminosities.
Independent checks are provided by radio galaxies and observations of Type II supernovae.
3 The spectra of light emitted by the stars of distant galaxies is redshifted, such that the redshift, z, is proportional to the distance of the galaxy.
4 This cosmological redshift finds a natural explanation in terms of the galaxies receding from us (and from each other), in accordance with Hubble's law. This is the first indication that the Universe began with a big bang.
5 Radio astronomers have detected microwave radiation (i.e. radiation with wavelengths in the region of 1 cm) coming almost isotropically from all directions, with a thermal spectrum which tallies, as far as can be measured, with that expected from calculations based on the big bang model. No convincing alternative explanations have so far been advanced. This 3 K radiation therefore provides good evidence both for there having been a big bang, and for the isotropy of the Universe at the time when the radiation decoupled from matter, 4 × 105 years later.
6 If the Earth at present is moving with respect to the 3 K radiation, which we assume is the same as the ‘rest frame’ of the Universe at the time of decoupling, the angular distribution of the intensity of the radiation would be slightly distorted in a characteristic way. Measurements indicate that the Earth does have such a velocity, with a magnitude of about 400 km s−1.
7 If galaxies, or clusters of galaxies, had already begun to form at a time considerably less than 107 years after the big bang, one would have expected pre-existent inhomogeneities in the matter distribution to have left a trace of their presence by imparting some intensity variation to the angular distribution of the 3 K radiation. Such inhomogeneities have now been detected at the level of 1 part in 100 000.
8 If there has been a hot big bang, we would expect the material produced to consist of 23% by mass of helium, the rest being mostly hydrogen, with traces of other light elements.
9 Detailed comparisons of predicted primordial nuclear mass fractions with those deduced from observations also constrain the value of the present-day baryonic mass density. A value of 4 or 5 ×10−28 kg m−3 fits well with both the nuclear abundance data and the data on anisotropies in the cosmic microwave background radiation.