An Open Singularity-Free Cosmological Model with Inflation

Authors: KORAY KARACA, SELÇUK BAYIN

Abstract: In the light of recent observations which point to an open universe (\Omega _{0} < 1), we reconsider singularity-free models, originally constructed for closed universes. Our model starts from a nonsingular state called prematter, governed by an inflationary equation of state P=( \gamma _{p}-1) \rho , where \gamma _{p} is a small positive parameter representing the initial vacuum dominance of the universe. Unlike the closed models, an open universe cannot be initially static hence, starts with an initial expansion rate represented by the initial value of the Hubble constant H(0). Therefore, our model is a two-parameter universe model (\gamma _{p},H(0)). During the prematter phase, due to the unusual characteristic of the equation of state, the universe heats up even though it expands. When the temperature in the universe reaches the Planck temperature T_{pl}, which is taken as the maximum attainable physical temperature, a first order phase transition carries the universe into the radiation era. Then the universe starts to behave as predicted in the standard model. The model proposed in this work predicts a value between 60 and 80 Km\cdot \sec ^{-1}\cdot Mpc^{-1} for the present value of the Hubble constant H_{0}, and the predicted value of \Omega _{0} lies between 0.3 and 0.6. Comparing the predictions of this model for the present properties of the universe with the recent observational results, we argue that the model constructed in this paper could be used as a realistic universe model.

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