Can the acceleration of our universe be explained by the effects of inhomogeneities?

No, it is simply not plausible that cosmic acceleration could arise within the context of general relativity from a back-reaction effect of inhomogeneities in our universe, without the presence of a cosmological constant or 'dark energy'. We point out that our universe appears to be described very accurately on all scales by a Newtonianly perturbed FLRW metric. (This assertion is entirely consistent with the fact that we commonly encounter δρ/ρ > 1030.) If the universe is accurately described by a Newtonianly perturbed FLRW metric, then the back-reaction of inhomogeneities on the dynamics of the universe is negligible. If not, then it is the burden of an alternative model to account for the observed properties of our universe. We emphasize with concrete examples that it is not adequate to attempt to justify a model by merely showing that some spatially averaged quantities behave the same way as in FLRW models with acceleration. A quantity representing the 'scale factor' may 'accelerate' without there being any physically observable consequences of this acceleration. It also is not adequate to calculate the second-order stress-energy tensor and show that it has a form similar to that of a cosmological constant of the appropriate magnitude. The second-order stress-energy tensor is gauge dependent, and if it were large, contributions of higher perturbative order could not be neglected. We attempt to clear up the apparent confusion between the second-order stress-energy tensor arising in perturbation theory and the 'effective stress-energy tensor' arising in the 'shortwave approximation'