https://doi.org/10.1140/epjc/s10052-021-08916-0
Regular Article – Theoretical Physics
Cosmology of cubic galileon in modified teleparallel gravity
Laboratory of Theoretical physics (LPTH) and Department of Physics, Faculty of Exact and Computer Science, Mohamed Seddik Ben Yayia university, Bp 98, Ouled Aissa, 18000, Jijel, Algeria
Received:
25
November
2020
Accepted:
24
January
2021
Published online:
2
February
2021
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 
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 
CDM model and the latest measurement.
© The Author(s) 2021
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Funded by SCOAP3
