einstein-aether scalar-tensor

The primary purpose of this study is to investigate the constant-roll inflationary scenario with anisotropic conditions concerning the Einstein-aether Scalar-tensor Cosmology in noncommutative phase space. We first introduce an Einstein-aether scalar-tensor cosmological model. In this structure, one can introduce an aether field with aether coefficients in the action integral of scalar-tensor. It will be a function of the scalar field, which is, in fact, a kind of extender of the Lorentz-violating theories. Hence, we present the point-like Lagrangian, which represents the field equations of the  Einstein-aether scalar-tensor model. Then we calculate the Hamiltonian of our model directly. According to the noncommutative phase space characteristics, we will calculate the specific equations of this model. Then, according to the constant-roll conditions, we take the anisotropic constant-roll inflationary scenario and calculate some cosmological parameters of the mentioned model, such as the Hubble parameter, potential, etc.