LRS Bianchi I model with constant deceleration parameter

Abstract

An LRS Bianchi I model is considered with constant deceleration parameter, $q=\alpha-1$, where $\alpha\geq0$ is a constant. The physical and kinematical behaviour of the models for $\alpha=0$ and $\alpha\neq0$ 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 $0.2\lesssim z\lesssim0.5$. 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 required to accommodate the early inflationary epoch caused by phantom matter. The models with $1<\alpha<3$ describe decelerating phases which are usually occur in the presence of dust or radiation. These models are also found anisotropic at early times and attain isotropy at late times. The model for $\alpha=3$ represents a stiff matter era which also has shear at early stages and becomes shear free at late times, but it evolves with an insignificant ceaseless anisotropy. The models with $\alpha>3$ violate the DEC and the corresponding scalar field models have negative potential which is physically unrealistic.