Horizon problem and inflation

In hot Big Bang models, the comoving region over which the CMB is observed to be homogeneous to better than one part in 105 at the last-scattering surface is much larger than the intersection of this surface with the future light cone from any point pB of the Big Bang. Since this light cone provides the maximal distance over which causal processes could have propagated from pB, the observed quasiisotropy of the CMB remains unexplained. As shown by Célérier (2000b), this ‘horizon problem’ develops sooner or later in any cosmological model exhibiting a spacelike singularity such as that occurring in the standard FLRW universes.

Even inflation, which was put forward in order to remove this drawback in the framework of standard homogeneous cosmology, only postpones the occurrence of the horizon problem, since it does not change the spacelike character of the singularity and is insufficient to solve it permanently. This is shown in Fig. 6.1, where thin lines represent light cones and where the CMB as seen by an observer O corresponds to the intersection of the observer's backward light cone with the last-scattering line. For a complete causal connection to occur between every pair of points in this intersection segment, all backward light signals issuing from points therein must reach the vertical axis before they reach the space like Big Bang curve. The event L is thus a limit beyond which any observer experiences the horizon problem. Adding an inflationary phase in the primordial history of the universe amounts to adding a slice of de Sitter spacetime, indicated here by the region between the dashed line and the Big Bang.