  We discuss cosmological models for an eternal universe. Physical observables
show no singularity from the infinite past to the infinite future. While the
universe is evolving, there is no beginning and no end - the universe exists
forever. The early state of inflation is described in two different, but
equivalent pictures. In the freeze frame the universe emerges from an almost
static state with flat geometry. After entropy production it shrinks and
"thaws" slowly from a "freeze state" with extremely low temperature. The field
transformation to the second "big bang picture" (Einstein frame) is singular.
This "field singularity" is responsible for an apparent singularity of the big
bang. Furthermore, we argue that past-incomplete geodesics do not necessarily
indicate a singularity or beginning of the universe. Proper time ceases to be a
useful concept for physical time if particles become massless. We propose to
define physical time by counting the number of zeros of a component of the wave
function. This counting is independent of the choice of coordinates and frames,
and applies to massive and massless particles alike.
