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E. P. Tryon (Hunter College and Graduate Center of The City University of New York)
A new set of cosmological spacetimes with galactic sheets and voids is being developed. Einstein's field equations are solved (in four dimensions) by an iterative procedure that converges rapidly for relevant values of input parameters. A few of the simplest solutions have already been obtained. They display a remarkable feature: space is virtually flat over cosmological distances for arbitrary values of Omega (with the cosmological constant regarded as vacuum energy contributing to Omega). Virtual flatness is readily seen to be a feature of all spacetimes in the set, which comprises a considerable variety of sheets and voids.
This work demonstrates that linkage between geometry and Omega is not a robust prediction of general relativity, but only a special feature of Friedmann models (apparently arising from their simplifying assumption of perfect homogeneity). Cosmological interpretations of data that have assumed the traditional Friedmann relation between geometry and Omega therefore require modification. Most obviously, standard inflation's prediction of flatness does not imply a critical density of mass-energy.
Acceleration (or deceleration) of the cosmic expansion is virtually the same as in Friedmann models for the simple solutions obtained thus far, but might conceivably be different for more complex structures and kinematics now under study.