Neutrinos are produced copiously in the primordial Universe and today they are the most abundant specie of particles after the photons. With the discovery of neutrinos oscillation it is known that at least two of them have mass, although the absolute values are unknown. The effects of massive neutrinos in the large scale structure formation have been much studied and the comparison with observational data establishes limits over the neutrinos mass sum. In this dissertation we broach other aspect of neutrinos in cosmology which has been few studied in literature: its influence in the global expansion and the possible observational implications. An interesting aspect of cosmic neutrinos background is that inside the present masses limits at least one specie must have passed from a relativistic regime to a non-relativist one, since the matter-radiation decoupling until now. This change in regime could cause observational effects characteristics of this process. In this research we investigate the neutrinos state equation in function of their mass and temperature. From this result, we obtain the expansion rate and the luminosity distance in function of the Universe red-shift considering the presence of massive neutrinos, besides the dark matter, cosmological constant and radiation. Even through we expect that the neutrinos impact in these observable be small, the objective of this work is to verify if it can be measured in the context of the emergent precision cosmology.