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In this paper, we explore the behaviors of scalar field in modified f (R, T ) gravity theory within the framework of a flat Friedmann-Robertson-Walker cosmological model. The universe is assumed to be filled with two noninteracting matter sources, scalar field (normal or phantom) with scalar potential and matter contribution due to f (R, T ) action. We first explore a model where the potential is a constant, and the universe evolves as a de Sitter type. This model is compatible with phantom scalar field only which gives fine tuning with the recent observations. The model exhibits a wide variety of early time physical phenomena that eventually behaves like a cosmological constant at late times. The model shows transition from decelerated to accelerated expansion of the universe. We also explore a model where the scalar field potential and the scale factor evolve exponentially as a scalar field. This model is compatible with normal scalar field only and describes transition from inflationary to the decelerated phase at early times and quintessence to phantom phase at late times. We constraint our results with the recent observational data and find that some values of parameters are consistent with SNe Ia and H (z) + SNe Ia data to describe accelerated expansion only whereas some one give decelerated and accelerated expansions with H (z), WMAP7 and WMAP7 + BAO + H (z) observational data.

An LRS Bianchi I model is considered with constant deceleration parameter, q = α − 1, where α ≥ 0 is a constant. The physical and kinematical behaviour of the models for α = 0 and α = 0 is studied in detail. The model with α = 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 z 0.5. The model obeys the "cosmic no hair conjecture". The models with 0 < α < 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 < α < 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 α = 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 α > 3 violate the DEC and the corresponding scalar field models have negative potential which is physically unrealistic.

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