Considering the entropic force on the holographic Hubble horizon of the universe which carries a Bekenstein-Hawking entropy and temperature leads to the entropic force cosmology, and it assumes that the entropic force is responsible from the increase of entropy and accelerated expansion of the universe as a source of cosmological constant. This assumption naturally solves the cosmological constant problem with the variable nature of the entropic pressure on the Hubble parameter. We investigate the implications of entropic force cosmology by obtaining the density parameters and the distance measures. Then, we generalize the model into higher dimensional universes in order to investigate the early period accelerations and density values of universe contents. After obtaining the density parameters, we find the luminosity distance and modulus equations. By comparing the luminosity distance values of standard.CDM and our model, we infer that the considered model presents a faster acceleration in the early periods of the universe implied from larger luminosity distances of the model for higher redshift values, which is completely supported by the inflationary paradigm. In addition, it is found that the luminosity distance becomes larger in higher dimensions for higher redshifts implying the early acceleration is larger. Moreover, from the distance modulus comparison of the model and the observational Gold Data, we find the considered model and its higher dimensional generalization are in accordance with the data, also the universe starts from higher dimensions with higher dark energy densities to lower compactified dimensions with lower dark energy densities, while the matter density increases. (C) 2021 Elsevier B.V. All rights reserved.