Holographic Dark Energy Model with Chaplygin Gas

Abstract

Recent cosmological observations namely, high redshift surveys of type Ia Supernovae, CMB etc. predict that the present universe is passing through an accelerating phase of expansion [1]. The discovery of anisotropy in the Cosmic Microwave Background (CMB) by the Cosmic Microwave Background Explorer (in short, COBE) satellite marked a major advance in cosmology. CMB anisotropy in general alongwith COBE data now provide some of the most powerful tests of cosmological theories, particularly theories concerning the formation of large-scale structure of the universe. It is now generally believed that the universe has emerged out of an inflationary phase in the past. It has been recently predicted that the present universe is undergoing an accelerating phse of expansion. The above two observational facts in the universe do not find explanation in the framework of Einstein general theory of Relativity (GTR) with normal matter. It is known that early inflation may be realized in a semiclassical theory of gravity where matter is described by quantum fields [2]. Starobinsky obtained inflationary solution considering a curvature squared term in the Einstein-Hilbert action [3] long before the advent of inflation was known. However, the efficacy of inflation is known only after the seminal work of Guth who first employed the phase transition mechanism to accommodate inflation. Thereafter more than a dozen of inflationary model came up. The early inflationary universe can be realized either by (i) a modification of gravitational sector of action introducung higher order terms or [4], (ii) a modification of the matter sector instead of perfect fluid, matter is described by quantum fields. Another way of realizing inflation is to consider imperfect fluid. In the case of matter, the equation of state (in short, EOS) is p = ω ρ where p represents the pressure and ρ represents the energy density, inflation is permitted if ω = −1. For a homogeneous scalar field the condition for inflation is achieved when the potential energy of the field dominates over the kinetic energy. The inflationary period ends when the scalar field or the inflaton field reaches the minimum of the potential. Thereafter the field oscillates and a small comoving volume grows to accommodate the whole universe. The universe decelerates during matter dominated era but the recent observation is that the universe is accelerating. The present accelerating phase can be realized with EOS parameter ω < −1. The usual fields in the standard model of particle physics are not suitable to obtain such accelerating phase of the present universe. In fact it is a challenge 5