The Eternal Closed Universe: Deflation-Inflation

Abstract: An outgrowth of the idea of inflation is advanced. In the inflation regime, the singularity condition is broken. Equations which govern inflation are invariant under time reversal, so that they describe deflation as well. Those two observations suggest that inflation may be extended to the following process: deflation (t<0)--minimum radius >0 (t=0)--inflation (t>0), with no singularity. A relevant construction is carried out in the framework both of classical and of reductive semiclassical gravity. The construction results in an eternal (-\infty<t<\infty) contracting-expanding closed universe.