CMB observations in LTB universes: Part I: Matching peak positions in the CMB spectrum

TL;DR

This paper investigates how inhomogeneous LTB cosmological models can match CMB peak positions and potentially explain accelerated expansion without dark energy, highlighting the impact of local inhomogeneities on cosmological parameter estimation.

Contribution

It constructs LTB models matching the concordance model's distance-redshift relation and demonstrates how modifying these models can fit CMB peak positions, challenging the need for dark energy.

Findings

LTB models can replicate the distance-redshift relation of the concordance model.

Adjusting the LTB model at high redshift can fit CMB peak positions.

Local inhomogeneities may influence the inferred cosmological parameters.

Abstract

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.