Annu. Rev. Astron. Astrophys. 1991. 29: 325-362 Copyright © 1991 by Annual Reviews. All rights reserved

2.2 Some Puzzling Features of the FRW Models

The problematic features of the standard hot big-bang model can be briefly summarized as follows:

2.2.1. THE HORIZON PROBLEM The typical fundamental observer O at a given epoch t has his past light cone truncated at t = 0, the epoch of the big-bang. A light signal in the radiation-dominated era could have only travelled a proper distance

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during the time interval (0, t). Thus, any causal communication to O is limited by a sphere of radius R_H centered on O. This boundary is called the particle horizon. Two observers O and O', separated by a proper distance larger than 2R_H (t) at epoch t, will therefore have totally disjoint spheres of communication (see Figure 1). Causal connection is a necessary requirement for establishing homogeneity across a large region. Therefore there is no a priori reason to expect O and O' to have a similar physical environment. In short, the existence of a particle horizon limits the physical processes that might have led to an attainment of homogeneity in the universe.

If the present features of the universe were essentially frozen at the GUTs epoch, we expect the sphere of radius 2R_H at that epoch to have expanded sufficiently to encompass the present observable universe with a size of about ~ 10²⁸ cm. (This would provide a natural explanation for the observed homogeneity of our universe.) Since the expansion factor increases in inverse proportion to temperature from the GUTs epoch (T ~ 10¹⁴ GeV) to the present MBR temperature of T₀ 2.4 x 10^-4 eV (= 2.75 K), the overall expansion is a factor 4 x 10²⁶. At t ~ 10^-35 s, however, 2R_H ~ 6 x 10^-25 cm. Thus the primordial sphere of homogeneity would have expanded only to a radius of about 2.4 x 10² cm, a value far short of the size of the present universe. So the presently observed large scale isotropy of the MBR and the very large scale homogeneity of discrete structures cannot be explained unless one postulates homogeneity at some initial epoch. The discrepancy is progressively reduced as one moves this epoch away from the big bang but is significant even when it is taken as late as when the radiation decoupled from matter at the last scattering surface.

Figure 1. The particle horizons of O and O' at world points B and C are given by the segments of the t = 0 line where their past light cones interact it. In the situation illustrated above, O and O' are so far apart that their particle horizons are disjointed.