Probing violation of the Copernican principle via the integrated Sachs-Wolfe effect

摘要

Recent observational data of supernovae indicate that we may live in anunderdense region, which challenges the Copernican principle. We show that theintegrated Sachs-Wolfe (ISW) effect is an excellent discriminator betweenanti-Copernican inhomogeneous models and the standard Copernican models. As areference model, we consider an anti-Copernican inhomogeneous model thatconsists of two inner negatively curved underdense regions and an outer flatEinstein-de Sitter region. We assume that these regions are connected by twothin-walls at redshifts z = 0.067 and z=0.45. In the inner two regions, thefirst-order ISW effect is dominant and comparable to that in the concordantflat-Lambda models. In the outer Einstein-de Sitter region, the first-order ISWeffect vanishes but the second-order ISW effect plays a dominant role, whilethe first-order ISW effect is dominant in the flat-Lambda models at moderateredshifts. This difference can discrimate the anti-Copernican models from theconcordant flat-Lambda model. At high redshits, the second-order ISW effect isdominant both in our inhomogeneous model and the concordant model. In the outerregion, moreover, the ISW effect due to large-scale density perturbations witha present matter density contrast much less than 0.37 is negligible, while theeffect due to small-scale density perturbations (such as clusters of galaxies,superclusters and voids) with matter density contrast much larger than 0.37would generate anisotropies which are larger than those generated by the ISWeffect in the concordant model.