Warped products and FRW cosmology
  We study the Friedmann-Robertson-Walker cosmological model to investigate non-smooth curvatures associated with multiple discontinuities involved in the evolution of the universe, by exploiting Lorentzian warped product scheme. Introducing double discontinuities occurred at the radiation-matter and matter-lambda phase transitions, we also discuss non-smooth features of the spatially flat Friedmann-Robertson-Walker universe. 
Soon-Tae Hong