Cosmic transit in phantom massive Chern–Simons models: confrontations with astronomical observations

We study a two-fluid cosmological model in the context of a dynamical Chern–Simons modified massive gravity with a time-varying gravitation predicted from recent astronomical observations. The solutions of the Friedmann equation are hyperbolically characterized by a cosmic transition from deceleration to acceleration and a jerk parameter which tends toward unity at late times. We have discussed two independent cases characterized by both hyperbolic evolution of the scale factor and graviton mass [Formula: see text][Formula: see text]eV. Both models predict a very slow evolution of the gravitational constant and the crossing of the phantom-divide line. Confrontations with various recent astronomical observations including BBN+PP+BAO+SHOES data sets have been done to estimate the parameters of the model.