Beyond four dimensions: An extended study of f(R,T) theory with multidimensional metric

The present communication explores [Formula: see text]-dimensional cosmological models within the framework of the [Formula: see text] theory. The exploration is motivated by Kaluza–Klein theory, where the existence of extra dimensions becomes a focal point in understanding the fundamental forces of the universe. A cosmological model has been constructed by assuming Fractional quadratic deceleration parameter. [Formula: see text] and [Formula: see text] provide a crucial link between theoretical predictions and empirical observations. Through rigorous mathematical analysis and theoretical modeling, we investigate the implications of this extended gravitational theory on cosmic evolution and the structure of spacetime. Our findings shed light on the interplay between geometry, matter and gravitational dynamics in multidimensional space, offering new insights into the nature of gravity and cosmological phenomenon.