Cosmological Issues in $F(T)$ Gravity Theory

We review recent developments on cosmology in extended teleparallel gravity, called “$F(T)$ gravity” with $T$ the torsion scalar in teleparallelism. We explore various cosmological aspects of $F(T)$ gravity including the evolution of the equation of state for the universe, finite-time future singularities, thermodynamics, and four-dimensional effective $F(T)$ gravity theories coming from the higher-dimensional Kaluza-Klein (KK) and Randall-Sundrum (RS) theories.