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Cosmic Acceleration from Topological Considerations

In this work we explore the possibility that the cosmological constant $\Lambda$ get a small value choosing appropriately the global topology of the universe. We explore some models, for example two concentric tree-dimensional spherical branes immersed in a five-dimensional space-time and find that the value for $\Lambda$ we observe in our universe could be small because it is the result of gravitational waves travelling in the 5D background produced during the collision of branes, in the beginning of the universe. In this model, like in the Epkyrotic, the Big Bang is caused for the collision of the branes. We discuss two different regimens where the energy density and the 5-dimensional cosmological constant are compared, with the aim to obtain the dynamics of the universe after and before the collision. Finally we obtain a dynamical solutions of the modify Friedmann equations as a result of a branes theory which proposed the existence of a quadratic term of the dark radiation in our brane which must be constraints on the spectrum of the CMB.

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