Acoustic peaks in the spectrum of the cosmic microwave background inspherically symmetric inhomogeneous cosmological models are studied. At thephoton-baryon decoupling epoch, the universe may be assumed to be dominated bynon-relativistic matter, and thus we may treat radiation as a test field in theuniverse filled with dust which is described by the Lema\^itre-Tolman-Bondi(LTB) solution. First, we give an LTB model whose distance-redshift relationagrees with that of the concordance $\Lambda$CDM model in the whole redshiftdomain and which is well approximated by the Einstein-de Sitter universe at andbefore decoupling. We determine the decoupling epoch in this LTB universe byGamow's criterion and then calculate the positions of acoustic peaks. Thusobtained results are not consistent with the WMAP data. However, we find thatone can fit the peak positions by appropriately modifying the LTB model,namely, by allowing the deviation of the distance-redshift relation from thatof the concordance $\Lambda$CDM model at $z>2$ where no observational data areavailable at present. Thus there is still a possibility of explaining theapparent accelerated expansion of the universe by inhomogeneity withoutresorting to dark energy if we abandon the Copernican principle. Even if we donot take this extreme attitude, it also suggests that local, isotropicinhomogeneities around us may seriously affect the determination of the densitycontents of the universe unless the possible existence of such inhomogeneitiesis properly taken into account.
展开▼
