In this paper we consider a quintom model of dark energy with a single scalar field T given by a Lagrangian which inspired by tachyonic Lagrangian in string theory. We consider non-minimal coupling of tachyon field to the scalar curvature, then we obtain the equation of state (EoS), and the condition required for the model parameters when ω crosses over −1.

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In this paper we consider a non-minimally coupled scaler field, and show its equation of state parameter can crossing over −1, ω → −1, and bouncing condition. Also we obtain the stability conditions and consider reconstructing for our model.

In this article in a generalization of our previous work, [1], we investigate the dynamics of the non-local F (R) gravity after casting it into local form. The non-singular bouncing behavior and quintom model of dark energy are achieved without involving negative kinetic energy fields. Two cosmological tests are performed to constrain the model parameters. In case of phantom crossing the distance modulus predicted by the model best-fits the observational data. In comparison with the CPL parametrization for drift velocity, the model in some redshift intervals is in good agreement with the data.

In this paper we consider FRW cosmology in modified non-local gravity. The stability analysis shows that there is only one stable critical point for the model and the universe undergoes a quintessence dominated era.