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LRS Bianchi I model with constant deceleration parameter

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Abstract

An LRS Bianchi I model is considered with constant deceleration parameter, \(q=\alpha -1\), where \(\alpha \ge 0\) is a constant. The physical and kinematical behaviour of the models for \(\alpha =0\) and \(\alpha \ne 0\) is studied in detail. The model with \(\alpha =0\) describes late time acceleration, but eternal inflation demands a violation of the NEC and WEC. The acceleration is caused by phantom matter which approaches a cosmological constant at late times. The solutions with a scalar field also show that the model is compatible with a phantom field only. A comparison with the observational outcomes indicates that the universe has entered into the present accelerating phase in recent past somewhere between \(0.2\lesssim z\lesssim 0.5\). The model obeys the “cosmic no hair conjecture”. The models with \(0<\alpha <1\) describe late time acceleration driven by quintessence dark energy. A violation of the NEC and WEC is The models with \(1< a < 3\) describe decelerating phases which are usually occur in the presence of dust or radiation. The models with \(\alpha >3\) violate the DEC and the corresponding scalar field models have negative potential which is physically unrealistic.

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Notes

  1. \(\rho +p\ge 0\).

  2. \(\rho +3p\ge 0\).

  3. The behavior of the Bianchi IX model is similar, provided that the cosmological constant must be large compared to the spatial curvature.

  4. \(\rho \ge 0\), \(\rho +p\ge 0\).

  5. The conjecture states that a large class of ever-expanding cosmological models with a positive cosmological constant rapidly approach asymptotically a de Sitter state at late times.

  6. If it is possible to enter into the inflationary phase well before the model recollapses, then all arguments still hold true for Bianchi IX also. However, this requires a comparison of two time scales that are strongly dependent on initial conditions.

  7. \(\rho \ge |p|\), i.e., \(\rho \pm p\ge 0\).

  8. Quantum theory and phantom scalar fields allow a negative potential in some contexts (see for example [87] and references therein).

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  1. Department of Mathematical Sciences, University of Zululand, Private Bag X1001, Kwa-Dlangezwa, 3886, South Africa

    Vijay Singh & Aroonkumar Beesham

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  1. Vijay Singh
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Singh, V., Beesham, A. LRS Bianchi I model with constant deceleration parameter. Gen Relativ Gravit 51, 166 (2019). https://doi.org/10.1007/s10714-019-2650-y

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