Abstract
At cosmological scales the Universe looks isotropic and homogeneous, although there exist structures and empty space. One of the mechanisms for the spacetime evolution of the universe (not for its creation) is the inflation, proposed by Alan Guth, by means of which the universe experienced an accelerated expansion in fractions of a second and let the energetic content continue evolving until acquiring the structure that we may observe today. The scenarios that many scientists have proposed, including Guth, are based on a fundamental scalar field called inflaton that ignites the primordial inflationary engine, maintaining the homogeneity and isotropy inherent to the nature of the field. In nature, those fields have not been observed yet, and this is the main motivation for searching another alternative that generates inflation, being one of them the vector fields. The aim of this work is to study the slow-roll inflation using primordial vector fields that maintain the characteristics of homogeneity and isotropy associated to the statistics of the large-scale structure, properties that have been observationally confirmed and predicted by the Hubble law. This, in turn, leads to solve the classical problems of the standard cosmology.
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