Exponential Scale Factor, F(T) Teleparallel Gravity, Entropy of Apparent Horizon and Cosmology

The equation for the function F(T) within the teleparallel gravity with torsion field T which provides the exponential scale factor is obtained and the function F(T) was computed. It is shown that the deceleration parameter q0 ≈ -0.535 according to the Planck data at the current epoch, can not be realized for cosmology based on the exponential scale factor. Therefore, models of cosmology based on the exponential scale factor (studied in many papers) is ruled out. In the framework of entropic cosmology, the associated entropy was found.