On complete maximal hypersurfaces in Robertson-Walker spacetimes with flat fiber

In this talk, we will deal with complete maximal hypersurfaces in spatially open $(n+1)$-dimensional Robertson-Walker spacetimes with flat fiber. Indeed, under natural geometric and physical assumptions we will obtain a new Calabi-Bernstein type result for these hypersurfaces as well as some nonexistence ones. To conclude, we will also apply these results to some relevant spacetimes, such as the steady state spacetime, the Einstein-de Sitter spacetime and certain radiation models.