Recent observational data of supernovae indicate that we may live in an underdense region , which challenges the Copernican principle .
We show that the integrated Sachs-Wolfe ( ISW ) effect is an excellent discriminator between anti-Copernican inhomogeneous models and the standard Copernican models .
As a reference model , we consider an anti-Copernican inhomogeneous model that consists of two inner negatively curved underdense regions and an outer flat Einstein-de Sitter region .
We assume that these regions are connected by two thin-walls at redshifts z = 0.067 and z = 0.45 .
In the inner two regions , the first-order ISW effect is dominant and comparable to that in the concordant flat- \Lambda models .
In the outer Einstein-de Sitter region , the first-order ISW effect vanishes but the second-order ISW effect plays a dominant role , while the first-order ISW effect is dominant in the flat- \Lambda models at moderate redshifts .
This difference can discrimate the anti-Copernican models from the concordant flat- \Lambda model .
At high redshits , the second-order ISW effect is dominant both in our inhomogeneous model and the concordant model .
In the outer region , moreover , the ISW effect due to large-scale density perturbations with a present matter density contrast \epsilon _ { m 0 } \ll 0.37 is negligible , while the effect due to small-scale density perturbations ( such as clusters of galaxies , superclusters and voids ) with \epsilon _ { m 0 } \gg 0.37 would generate anisotropies which are larger than those generated by the ISW effect in the concordant model .