This paper presents a new cosmological theory entitled the "Small Bang” model, a variation on the Big Bang theory, in which all of the energy and matter observed in the Universe are generated from the process of cosmic inflation. In the Small Bang model, each galaxy arises from a small seed given by an antimatter micro black hole. In the cosmic inflation process this micro black hole grows exponentially, breaking up pairs of virtual particles and attracting those composed by antimatter, while repelling the matter particles relying on matter-antimatter repulsion interactions. At the culmination of this process, a rotating matter cloud is formed and at its center is an Antimatter Super Massive Black Hole (ASMBH). The effect of the ASMBH mass over the galaxy rotation is very small. However if we consider that the ASMBH has a large angular momentum, a significant influence over the galaxy rotation should be observed. Thus, the authors believe that the effects currently attributed to some kind of Dark Matter, can be explained in a model that considers the mass and angular momentum of the ASMBH that exists at the center of each galaxy. The Small Bang model also explains some open points in the Big Bang standard theory, like the missing antimatter in the galaxy, the galaxy formation process and the relation between the super massive black hole’s mass and the galaxy mass. This new model also eliminates problems associated with the initial black hole singularity, like infinite temperature, by proposing a Universe that starts with an empty and cold space with a Planck length diameter. The Small Bang model also represents an innovation to the Big Bang model that has remained virtually unchanged for over 70 years. These new ideas have potential to change the way cosmologists perceive the forming of galaxies and of our Universe.