Consider the following FLRW spacetime: ds^2 = −dt^2 + t ^2/ t ^2 ∗ (dx^2 + dy^2 + dz^2 ), where t∗ is a constant. a) State whether this universe is spatially open, closed or flat. a) State whether this universe is spatially open, closed or flat. b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function of time t, starting at t = 0. c) Taking galaxy A to be located at (x, y, z) = (0, 0, 0), determine the proper distance to galaxy B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect to galaxy A.

Consider the following FLRW spacetime: ds^2 = −dt^2 + t ^2/ t ^2 ∗ (dx^2 + dy^2 + dz^2 ), where t∗ is a constant. a) State whether this universe is spatially open, closed or flat. a) State whether this universe is spatially open, closed or flat. b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function of time t, starting at t = 0. c) Taking galaxy A to be located at (x, y, z) = (0, 0, 0), determine the proper distance to galaxy B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect to galaxy A.