Toward a No-Go Theorem for an Accelerating Universe through a Nonlinear Backreaction

The backreaction of nonlinear inhomogeneities to the cosmic expansion isre-analyzed in the framework of general relativity. Apparent discrepanciesregarding the effect of the nonlinear backreaction, which exist among theresults of previous works in different gauges, are resolved. By defining thespatially averaged matter energy density as a conserved quantity in the largecomoving volume, it is shown that the nonlinear backreaction neitheraccelerates nor decelerates the cosmic expansion in a matter-dominateduniverse. The present result in the Newtonian gauge is consistent with theprevious results obtained in the comoving synchronous gauge. Although our workdoes not give a complete proof, it strongly suggests the following no-gotheorem: No cosmic acceleration occurs as a result of the nonlinearbackreaction via averaging.Comment: 6 pages (PTPTeX); accepted for publication in Prog. Theor. Phys; minor changes to match published versio