A Universe without expansion
  We discuss a cosmological model where the universe shrinks rather than
expands during the radiation and matter dominated periods. Instead, the Planck
mass and all particle masses grow exponentially, with the size of atoms
shrinking correspondingly. Only dimensionless ratios as the distance between
galaxies divided by the atom radius are observable. Then the cosmological
increase of this ratio can also be attributed to shrinking atoms. We present a
simple model where the masses of particles arise from a scalar "cosmon" field,
similar to the Higgs scalar. The potential of the cosmon is responsible for
inflation and the present dark energy. Our model is compatible with all present
observations. While the value of the cosmon field increases, the curvature
scalar is almost constant during all cosmological epochs. Cosmology has no big
bang singularity. There exist other, equivalent choices of field variables for
which the universe shows the usual expansion or is static during the radiation
or matter dominated epochs. For those "field coordinates" the big bang is
singular. Thus the big bang singularity turns out to be related to a singular
choice of field coordinates.
