  We investigate a particular type of classical nonsingular bouncing cosmology,
which results from general relativity if we allow for degenerate metrics. The
simplest model has a matter content with a constant equation-of-state parameter
and we get the modified Hubble diagrams for both the luminosity distance and
the angular diameter distance. Based on these results, we present a
Gedankenexperiment to determine the length scale of the spacetime defect which
has replaced the big bang singularity. A possibly more realistic model has an
equation-of-state parameter which is different before and after the bounce.
This last model also provides an upper bound on the defect length scale.
