CMB observations in LTB universes: Part I: Matching peak positions in
  the CMB spectrum
  Acoustic peaks in the spectrum of the cosmic microwave background in
spherically symmetric inhomogeneous cosmological models are studied. At the
photon-baryon decoupling epoch, the universe may be assumed to be dominated by
non-relativistic matter, and thus we may treat radiation as a test field in the
universe filled with dust which is described by the Lema\^itre-Tolman-Bondi
(LTB) solution. First, we give an LTB model whose distance-redshift relation
agrees with that of the concordance $\Lambda$CDM model in the whole redshift
domain and which is well approximated by the Einstein-de Sitter universe at and
before decoupling. We determine the decoupling epoch in this LTB universe by
Gamow's criterion and then calculate the positions of acoustic peaks. Thus
obtained results are not consistent with the WMAP data. However, we find that
one can fit the peak positions by appropriately modifying the LTB model,
namely, by allowing the deviation of the distance-redshift relation from that
of the concordance $\Lambda$CDM model at $z>2$ where no observational data are
available at present. Thus there is still a possibility of explaining the
apparent accelerated expansion of the universe by inhomogeneity without
resorting to dark energy if we abandon the Copernican principle. Even if we do
not take this extreme attitude, it also suggests that local, isotropic
inhomogeneities around us may seriously affect the determination of the density
contents of the universe unless the possible existence of such inhomogeneities
is properly taken into account.
