  Considering radial geodesics in the Robertson-Walker metric leads us to
abandon the co-moving coordinates. Instead we work in the cosmic rest frame.
Since then the matter is in motion, the solution of Einstein's equations is
more complicated. We calculate the first correction to standard cosmology which
has an off-diagonal term b dt dr in the metric. It describes the late universe.
We then solve Maxwell's equations in the new metric and discuss redshift and
luminosities. We obtain the correct age of the universe T=14 Gyr= 1/H, without
assuming a cosmological constant.
