Conformal symmetries driven exact higher-dimensional Kaluza-Klein cosmological solutions and in non-conservative gravitational framework

In this study, we investigate a five-dimensional Kaluza–Klein spacetime within the framework of f ( R, T ) gravity. The corresponding field equations are solved to obtain a variety of cosmological solutions, including a linear extra-dimensional vacuum solution, an expanding compact extra-dimensional solution, a uniformly linearly expanding solution, a linear isotropic solution, a logarithmic extra-dimensional solution, and a non-singular logarithmic extra-dimensional solution. The physical characteristics of these models are analyzed in terms of key cosmological quantities, namely the spatial volume, the mean Hubble parameter, the expansion scalar, the shear scalar, and the deceleration parameter. Moreover, the conformal vector fields (CVFs) associated with the obtained metrics are derived via a direct integration method. It is found that, for certain classes of solutions, the conformal symmetry algebra attains its maximal dimension of twenty-one, revealing a particularly rich symmetry structure of the underlying higher-dimensional geometry. To the best of our knowledge, such cosmological solutions, together with their corresponding CVFs in the context of f ( R, T ) gravity, have not been previously reported in the literature. Consequently, the derivation of these solutions and the systematic determination of their CVFs constitute the principal contribution and novelty of the present work.