Bianchi Type VI0 Inflationary Universe with Constant Deceleration Parameter and Flat Potential in General Relativity

Abstract

Abstract. Inflationary universe scenario with constant deceleration parameter in the presence of massless scalar field and flat potential taking Bianchi Type VI 0 space time as a source is discussed. We find that the rate of expansion slows down with increase of time. It is also observed that the ratio of shear and expansion is non-zero for all values of T where at + b = T, t being cosmic time, a and b being constants. Thus the universe remains anisotropic throughout the evolution. The Higgs field is constant for large values of T when α < 2 and the Higgs field evolves slowly but the universe expands for α > 2 where α is a constant. It may be positive and negative both. The model represents decelerating and accelerating phases of universe and has Point Type singularity at T=0 (MacCallum [25]). In special case i.e. if N=0 and α > 0 then the model isotropizes at late time, N being constant of integration.Keywords: Bianchi VI 0 , Inflationary, deceleration parameter, flat potential IntroductionThe primordial acceleration in which the universe undergoes rapid exponential expansion is known as inflation. The notion of inflation is so far one of the best mechanism at the early stages of evolution of the universe to explain the flat, homogeneous and isotropic nature of the present day universe. In these models, the universe undergoes a phase transition characterized by the evolution of Higgs field φ. The inflation will take place if potential V(φ) has flat region and in this region, the Higgs field φ evolves slowly but the universe expands in an exponential way due to vacuum field energy. The flat part of the potential is naturally associated with a vacuum energy that is identified as an effective cosmological constant (Ʌ) which makes the universe enter an inflationary period. Historically, a model closely related to the inflationary universe was suggested by Starobinsky [1] but the inflationary cosmological models became popular after an important paper of Guth [2] who proposed inflationary model in the context of grand unified field theory (GUT). There are two basic types of inflationary models: one is due to appearance of a flat potential e.g. in GUT's phase transitions and the other is due to a scalar curvaturesquarred term. Barrow and Turner [3] pointed out that a universe with a large amount of anisotropy will not undergo the inflationary phase. A universe with only moderate anisotropy will undergo inflation and will be rapidly isotropized. Sato [4] in a study has shown that the most prevailing inflationary models are investigated through the scalar field which acts as a source of inflation and generates cosmic acceleration. Inflationary scenario for homogeneous and isotropic models (FRW models) has been studied by many authors viz. The universe in smaller scale is neither homogeneous nor isotropic nor do we expect the universe to have these properties in its early stages. Also Astronomical observations in late eighties revealed that the predictions of FRW models do not always meet our requirements as were believ...