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We explore the four-dimensional effective $F(T)$ gravity with $T$ the torsionscalar in teleparallelism originating from higher-dimensional space-timetheories, in particular the Kaluza-Klein (KK) and Randall-Sundrum (RS)theories. First, through the KK dimensional reduction from the five-dimensionalspace-time, we obtain the four-dimensional effective theory of $F(T)$ gravitywith its coupling to a scalar field. Second, taking the RS type-II model inwhich there exist the five-dimensional Anti-de Sitter (AdS) space-time withfour-dimensional Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) brane, we findthat there will appear the contribution of $F(T)$ gravity on thefour-dimensional FLRW brane. It is demonstrated that inflation and the darkenergy dominated stage can be realized in the KK and RS models, respectively,due to the effect of only the torsion in teleparallelism without that of thecurvature.

Effective $F(T)$ gravity from the higher-dimensional Kaluza-Klein and Randall-Sundrum theories