Toward a No-go theorem for accelerating universe by nonlinear backreaction

Backreaction of nonlinear inhomogeneities to the cosmic expansion is analyzed in the framework of general relativity. In order to pay special attention to the gauge issues, the calculation is done in the Newtonian gauge. By defining the spatially averaged matter energy density as a conserved quantity in the large comoving volume, it is shown that the nonlinear backreaction neither accelerates nor decelerates the cosmic expansion in a matter-dominated universe. The conclusion is consistent with the previous works done in the comoving synchronous gauge. Although our work does not give a complete proof, it strongly suggest the following no-go theorem: no cosmic acceleration occurs due to nonlinear backreaction via averaging.