The primordial nucleosynthesis process has been studied in cosmology since the forties, when Alpher, Bethe and Gamov described the reactions that could take place in the expanding universe represented by FRW metric. From this moment, the computations of light nuclei abundances have been improved with numerical techniques but also with astrophysical developments. However, it is imperative to upgrade the calculated abundances. In this work, we consider the influence of sterile neutrinos, as a contribution of dark matter in radiation domination and their effects in the Hubble factor H, through relativistic degrees of freedom, to compute the relative abundances of primordial nuclei that were produced in cosmological nucleosynthesis by solving the Boltzmann equation. In addition, we make a comparison between our results and the WMAP values for ²H, ³He, ⁴He and ⁷Li abundances.