Hubble spheres and particle horizons

Abstract

Isotropy of the cosmic microwave background radiation highlights the horizon problem. Analysis of the horizon problem and its inflationary solution requires that we study the properties of the Hubble sphere and distinguish between the "Hubble surface" and the particle horizon. All regions in the visible universe become causally connected when inflation increased the distance of the particle horizon by a factor of 3. If exponential inflation occurs because of a phase transition at temperature ~10 15 GeV, the number of ^-foldings to effect this threefold increase in the particle horizon distance is N ~ 60. The properties of the Hubble sphere provide the answer to the question: How, in a universe of age i, can regions separated by distances much greater than ct be causally connected? Subject headings: cosmology-relativity