Classical bouncing Universes from vector fields

Abstract

For the anisotropic Universe filled with massless vector field in the General Relativity frame we obtain bouncing solution for one of scale factors. We obtain the Universe with finite maximal energy density, finite value of $R,R^{\mu\nu}R_{\mu\nu},R^{\mu\nu\alpha\beta}R_{\mu\nu\alpha\beta}$ and non-zero value of a scale factor for directions transverse to a vector field. Such a bounce can be also obtained for a massive vector field with kinetic initial conditions, which gives isotropic low energy limit. We discuss the existence of a bounce for a massless vector field with additional matter fields, such as cosmological constant or dust. We also discuss bouncing solution for massless vector field domination in $n+2$ dimensional space-time.