In this present paper, a slowly rotating stat is investigated in shift symmetric scalar torsion theory framework using a nondiagonal tetrad that gives an axially symmetric spacetime. We present the general equations for a general Lagrangian in a spherical symmetric space time and then in an axially symmetric spacetime. The obtained equations will allow us to study the behaviour of a specific model at the center of the star and at large distance. We find that this particular model affects the behaviour at the center but it is not case for large value of the radial coordinate r. The integration of the equations of motion, for different realistic equations of state (EoS), confirms that the mass, the radius as well as the moment of inertia are effected by varying the parameters of the model. Finally, we examine the universal relation of normalized moment of inertia and the stellar compactness of neutron star in slow rotation approximation. We showed that for all values of parameters present in the model leads to a deviation from GR for all EoS with a relative deviation below $$10\%$$
10
%
.
In this present paper, we study the cosmological evolution of the cubic galileon along with modified teleparallel gravity at perturbed and non-perturbed levels. We show the dynamical equations of motion and investigate the evolution of different cosmological parameters by using the dynamical variables analysis. In addition, a detailed analysis of different cosmological evolution in the matter, radiation and de Sitter eras is presented by solving the dynamical equations numerically. In our analysis, we find that the equations of motion in the Friedmann–Robertson–Walker (FRW) background metric is characterized by a stable de Sitter era and a tracker solution in which $$H{\dot{\varphi }}$$
H
φ
˙
is always constant. We find also that the equation of state of dark energy associated to the proposed model in this work can deviate from − 2 at the matter era. Moreover, the conditions of avoiding ghost and Laplacian instabilities in our model are derived; then we show that the model is free of these instabilities. Furthermore we place an observational constraint on the parameters of the model through Monte Carlo numerical method using growth rate and observational Hubble data. Finally, using the best-fit values of parameters in the model we compare our growth rate of matter perturbation with the prediction of $$\varLambda $$
Λ
CDM model and the latest measurement.
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