Evolution of cosmological event horizons in anisotropic universes

Abstract

We study the evolution of cosmological event horizons in anisotropic Kasner universes in the presence of a positive cosmological constant by analyzing null geodesics. At later times, the asymptotic form of cosmological horizons is the same spherical surface as the de Sitter horizon. At the early times, however, it has non-spherical shape with its eccentricity decreases with time. The horizon area increases with time respecting the second law of thermodynamics. The initial shape of the cosmological horizon takes the form of a needle or pancake surface depending on the nature of the background spacetimes. We also discuss that the presence of the holographic dark energy will modify significantly the initial evolution of the anisotropic universes.PACS numbers: 98.80. Bp,98.80.Jk Following the Copernican principle [1], the physical properties of the universe are spatially homogeneous viewed on a sufficiently large scale. This is consistent with nowadays experiments up to of order 10 −5 . Based on the principle, the Robertson-Walker spacetime with inflation at early stage, on which small perturbations evolve to give cosmological structures, is widely used to describe the present universe. However, there is no reason to believe that our universe was initially homogenous and isotropic. Generically, it could be highly inhomogeneous and anisotropic. The cosmic no-hair theorem [2] shows that in the presence of inflation most of the initially anisotropic cosmological spacetimes become isotropic rapidly if the matter fields residing in the universe satisfy the dominant energy condition. The theorem also implies that it is inevitable to have a highly anisotropic pre-inflationary universe if any small anisotropy remains after inflation. Since the anisotropy will be exponentially enhanced if we observe the universe backward in time and we cannot make that process stop by adding ordinary matters or radiations. The vestige of the pre-inflationary anisotropies can be seen through the large scale anomalies in the WMAP power spectra if the e-folding of inflation is not larger than 64 for GUT scale inflation. [3,4]. In fact, there is possibility that the effect of pre-inflationary anisotropies has been already detected in the Cosmic Microwave Background (CMB) temperature anisotropies, as an apparent alignment of the CMB multipoles on very large scales, so-called "Axis of Evil" [5-10] and giant rings [11].The standard cosmological model is the Λ-CDM model where most part of the universe is composed of the cosmological constant and cold dark matters. The spacetime has a future event horizon located at a distance R h = a(τ )where a(τ ) is the scale factor of the Robertson-Walker metric and τ is the comoving time. In the presence of asymptotically accelerating expansion of the universe, any observers will be surrounded by the future event horizon, which restricts the observers access to the information of the universe. This lack of information is represented by a kind of entropy proportional to the area of the cosmological horizon div...