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We present a brief review of the modified Brans-Dicke theory (MBDT) in arbitrary dimensions, whereby the ($N+1$)-dimensional field equations reduce to the $N$-dimensional $(ND)$ configuration with sources and an effective induced scalar potential. We then investigate a generalized Bianchi type~I anisotropic cosmology in $5D$ BD theory that leads to an extended Kasner solution. By employing the original equations of MBDT, we probe the reduced Kasner cosmology on the hypersuface with proceeding the investigations for a few cosmological quantities, explaining their properties for some cosmological models.}

Kasner Solution in Brans–Dicke Theory and Its Corresponding Reduced Cosmology