In light of the cosmological observations, we investigate dark energy models from the Horndeski theory of gravity. In particular, we consider cosmological models with the derivative self-interaction of the scalar field and the derivative coupling between the scalar field and gravity. We choose the self-interaction term to have an exponential function of the scalar field with both positive and negative exponents. For the function that has a positive exponent, our result shows that the derivative self-interaction term plays an important role in the late-time universe. On the other hand, to reproduce the right cosmic history, the derivative coupling between the scalar field and gravity must dominate during the radiation-dominated phase. However, the importance of such a coupling in the present universe found to be negligible due to its drastic decrease over time. Moreover, the propagation speed of gravitational waves estimated for our model is within the observational bounds, and our model satisfies the observational constraints on the dark energy equation of state.
We investigate the regularized four-dimensional Einstein–Gauss–Bonnet (4DEGB) gravity with a non-minimal scalar coupling function, which is an extension of the regularized 4DEGB theory. By introducing non-minimal coupling to the Gauss-Bonnet term, we demonstrate the additional contribution to the dynamical equations which is otherwise absent in the dimensionally regularized theory. Furthermore, we analyze the stability of the system by using the dynamical system approach based on fixed points. Then, we consider time evolution to investigate the history of the universe and to constrain observational data to obtain the cosmological parameters of the model.
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