Cosmic acceleration from topological considerations III: Lie group.

Recent observations on the large-scale structure of the universe indicate that the cosmological constant cannot be the definitive answer to the nature of dark energy. Therefore, it is a good time to propose alternatives to understand the accelerated expansion of spacetime. In this work, we study the possibility that the accelerated expansion of spacetime is due to the topology of the universe. We assume that the topology of the universe is a principal fiber bundle, whose base space is our 4-dimensional spacetime and whose fiber is a N-dimensional compact semi-simple Lie group. We suppose a homogeneous and isotropic spacetime described by the Friedman-Robertson-Walker metric, and a fiber that evolves with respect to time and is endowed with a left-invariant metric. With this hypothesis, we find that these Lie groups cause an accelerated expansion of spacetime. Furthermore, we study the behavior of the deceleration parameter and the density parameters of matter and radiation.