Precision cosmology defeats void models for acceleration

The suggestion that we occupy a privileged position near the center of a large, nonlinear, and nearly spherical void has recently attracted much attention as an alternative to dark energy. Putting aside the philosophical problems with this scenario, we perform the most complete and up-to-date comparison with cosmological data. We use supernovae and the full cosmic microwave background spectrum as the basis of our analysis. We also include constraints from radial baryonic acoustic oscillations, the local Hubble rate, age, big bang nucleosynthesis, the Compton $y$ distortion, and for the first time include the local amplitude of matter fluctuations, ${\sigma }_8$. These all paint a consistent picture in which voids are in severe tension with the data. In particular, void models predict a very low local Hubble rate, suffer from an “old age problem,” and predict much less local structure than is observed.

Figure 1

Effective EdS parameters $T_0^{\mathrm{EdS}}$ and $H_0^{\mathrm{EdS}}$ as a function of the matter density ${\Omega }_{\mathrm{m}}$ in the corresponding $\Lambda \mathrm{CDM}$ cosmology are shown.

Figure 2

CMB power spectra for the WMAP7 $\Lambda \mathrm{CDM}$ cosmology (solid curves) along with the corresponding effective EdS model (dotted curves) are shown. We show the TT (top panel), polarization-polarization (EE) (middle panel), and TE (bottom panel) spectra.

Figure 3

Constraints on the effective EdS parameters from the CMB power spectrum data are shown. Likelihood contours show the 68% and 95% confidence levels. Dotted and solid contours are for models with and without spectral index running, respectively.

Figure 4

The local density parameter ${\Omega }_{\mathrm{m}}^{\mathrm{loc}}$ versus redshift $z$ for the spline (top panel), $\mathrm{\text{polynomial}}+\mathrm{\text{shell}}$ (middle panel), and $\mathrm{\text{polynomial}}+\mathrm{\text{curvature}}$ (bottom panel) profiles is shown. The grayscale level indicates the relative likelihood in the fit to the $\mathrm{CMB}+\mathrm{SN}$ data.

Figure 5

Selection of marginalized likelihoods for the $\mathrm{\text{polynomial}}+\mathrm{\text{shell}}$ profile using the $\mathrm{CMB}+\mathrm{SN}$ data are shown. For the Compton $y$ distortion the dashed curve shows the addition of radial BAO data, while the vertical line is the COBE $2\sigma$ upper limit [58].

Figure 6

The lookback time versus $z$ for the spline (top panel) and $\mathrm{\text{polynomial}}+\mathrm{\text{shell}}$ (bottom panel) profiles is shown. The $\mathrm{\text{polynomial}}+\mathrm{\text{curvature}}$ case is very similar. The dotted curve is the lookback time for the WMAP7 $\Lambda \mathrm{CDM}$ cosmology.

Figure 7

Dipole $\beta$ versus $z$ for the spline (top panel), $\mathrm{\text{polynomial}}+\mathrm{\text{shell}}$ (middle panel), and $\mathrm{\text{polynomial}}+\mathrm{\text{curvature}}$ (bottom panel) profiles is shown.

Figure 8

The radial BAO scale $\Delta z$ versus $z$ for the spline (top panel) and $\mathrm{\text{polynomial}}+\mathrm{\text{shell}}$ (bottom panel) profiles is shown. The $\mathrm{\text{polynomial}}+\mathrm{\text{curvature}}$ case is very similar to the $\mathrm{\text{polynomial}}+\mathrm{\text{shell}}$, but without the suppression at $z\sim 2$. Also shown (dotted curves) is the best-fit $\Lambda \mathrm{CDM}$ model, along with the measurements from Refs. 59, 60.

Figure 9

The high $\ell$ CMB spectrum is shown. The best-fit $\Lambda \mathrm{CDM}$ model is shown by the solid curve, the effective EdS with power-law spectrum by the dotted curve, and the effective EdS with fixed $T_0^{\mathrm{EdS}}=T_0$ and a broken power law by the dashed curve. Also shown is binned WMAP and ACBAR data.

Figure 10

The multivalued region of parameter space for the spline profile is shown. The top left panel has ${\Omega }_{\mathrm{m}}^{\mathrm{loc}}(z=0)=0.2$, top right 0.15, bottom left 0.1, and bottom right 0.05. Shaded contours show the reduced ${\chi }^2$ from a fit to SN data (note the different scale in the bottom right panel), and dashed contours the value of $100h_0$. The region at the bottom of each panel below the heavy solid line is the multivalued regime.

Figure 11

An example of a multivalued profile for ${\Omega }_{\mathrm{m}}^{\mathrm{loc}}(z=0)=0.05$ is shown. The top panel shows the density parameter and the bottom panel shows the SN magnitude residual, together with the Union2 data. The kind ${\chi }^2$ is significantly better than that of the single-valued solutions.

Figure 12

An illustration of SNe distributed in the multivalued region of the redshift-luminosity distance relation is shown. The horizontal axis is a measure of redshift.