The current model of the universe evolved from the geocentric model to the heliocentric model. This describes the shift from the belief that the Earth was at the center of the universe to the understanding that the Sun is at the center of our solar system, which paved the way for modern astronomy and our current understanding of the universe.
The other options mentioned (cyclic theory and big bang theory) refer to different theoretical frameworks regarding the universe's origin and fate, but they are not directly about the evolution of models from one to another in the same context as the geocentric and heliocentric models.