Searching for a Cosmological Preferred Axis in complicated class of cosmological models:Case study $f(R,T)$ model

Recent astronomical observations show that the universe may be anisotropic on large scales. The Union2 SnIa data hint that the universe has a preferred direction. If such a cosmological privileged axis indeed exists, one has to consider an anisotropic expanding Universe instead of the isotropic cosmological model. In this paper, we present a detailed analysis of the dark energy dipole in $f(R,T)=f_1(R)+f_2(T)$ Cosmological Model using three types of dipole fit (DF) method which are (I)dipole + monopole fitting for distance modulus(DMFDM), (II)dipole + monopole fitting for luminosity distance(DMFLD) and (III) general dipole fitting for luminosity distance(GDFLD). We have found the maximum anisotropic deviation direction for (DMFDM) method as $(l,b)=(315_{-25}^{+25},-23_{-15}^{+14})$, for (DMFLD) as $(l,b)=(l,b)=(315_{-37}^{+35},-23_{-18}^{+18})$, and for (GDFLD) method as $(l,b)=(317_{-32}^{+32},-23_{-18}^{+18})$ which are located very close to each other. We compare our model with the $CPL$, $\mathrm{\Lambda }CDM$ and $\omega CDM$ models. Constraints on $(l,b)$ in $f(R,T)$ model are not much different from the cases of the $CPL$, $\mathrm{\Lambda }CDM$ and $\omega CDM$ models. Moreover, the results are consistent with other studies.