Emergent Cosmology in Magnetized Bianchi VI Geometry within f(R, T) Gravity

In this paper, we have investigated the consequences of emergent cosmology in a magnetised Bianchi-VI spacetime in \(\varvec{f}(\varvec{R,T})\) $\mathit{f}(\mathit{R}\mathbf{,}\mathit{T})$ gravity. We thoroughly investigated the stability criteria in the context of emergent cosmology for the homogeneous and anisotropic Bianchi VI geometry in the simplest \(\varvec{f}(\varvec{R,T})\) $\mathit{f}(\mathit{R}\mathbf{,}\mathit{T})$ model of the type \(\varvec{f}(\varvec{R,T}) \varvec{= R + 2\zeta T + 2\Lambda _0}\) $\mathit{f}(\mathit{R}\mathbf{,}\mathit{T})\mathbf{=}\mathit{R}\mathbf{+}\mathbf{2}\mathit{\zeta }\mathit{T}\mathbf{+}\mathbf{2}{\mathbf{\Lambda }}_{\mathbf{0}}$ , in the presence of a non-zero cosmological constant \(\varvec{\Lambda _0}\) ${\mathbf{\Lambda }}_{\mathbf{0}}$ . It is found that the existence of a viable ESU within our framework requires the presence of positive cosmological constant. We studied the existence conditions of a non-singular ESU and carried on the study to investigate the dependence of the anisotropy parameter \(\varvec{k}\) $\mathit{k}$ on the dynamics of emergent cosmology as two independent models. Furthermore, we also studied the graceful exit mechanism for the models and found that the model with \(\varvec{k=2}\) $\mathit{k}\mathbf{=}\mathbf{2}$ shows promising results as a possible candidate of the emergent scenario whereas the model with \(\varvec{k=4}\) $\mathit{k}\mathbf{=}\mathbf{4}$ does not qualify as a viable candidate for describing the same. The stability analysis is further carried out in terms of the effective potential formalism and found specific regions for the EoS parameters and cosmological constants where the stability of the ESU exists and finally the stability of the model is tested against homogeneous scalar perturbation which shows perturbation remains finite rendering the ESU stable subject to these perturbation.