Memoirs of the American Mathematical Society 2012; 69 pp; softcover Volume: 218 ISBN10: 0821853589 ISBN13: 9780821853580 List Price: US$58 Individual Members: US$34.80 Institutional Members: US$46.40 Order Code: MEMO/218/1025
 The authors prove that the Einstein equations for a spherically symmetric spacetime in Standard Schwarzschild Coordinates (SSC) close to form a system of three ordinary differential equations for a family of selfsimilar expansion waves, and the critical (\(k=0\)) Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology is embedded as a single point in this family. Removing a scaling law and imposing regularity at the center, they prove that the family reduces to an implicitly defined oneparameter family of distinct spacetimes determined by the value of a new acceleration parameter \(a\), such that \(a=1\) corresponds to the Standard Model. The authors prove that all of the selfsimilar spacetimes in the family are distinct from the noncritical \(k\neq0\) Friedmann spacetimes, thereby characterizing the critical \(k=0\) Friedmann universe as the unique spacetime lying at the intersection of these two oneparameter families. They then present a mathematically rigorous analysis of solutions near the singular point at the center, deriving the expansion of solutions up to fourth order in the fractional distance to the Hubble Length. Finally, they use these rigorous estimates to calculate the exact leading order quadratic and cubic corrections to the redshift vs luminosity relation for an observer at the center. Table of Contents  Introduction
 Selfsimilar coordinates for the \(k=0\) FRW spacetime
 The expanding wave equations
 Canonical comoving coordinates and comparison with the \(k\neq0\) FRW spacetimes
 Leading order corrections to the standard model induced by the expanding waves
 A foliation of the expanding wave spacetimes into flat spacelike hypersurfaces with modified scale factor \(R(t)=t^{a}\)
 Expanding wave corrections to the standard model in approximate comoving coordinates
 Redshift vs luminosity relations and the anomalous acceleration
 Appendix: The mirror problem
 Concluding remarks
 Bibliography
