Reconciling the local void with the CMB

In the standard cosmological model, the dimming of distant Type Ia supernovae is explained by invoking the existence of repulsive “dark energy” which is causing the Hubble expansion to accelerate. However, this may be an artifact of interpreting the data in an (oversimplified) homogeneous model universe. In the simplest inhomogeneous model which fits the SNe Ia Hubble diagram without dark energy, we are located close to the center of a void modeled by a Lemaítre-Tolman-Bondi metric. It has been claimed that such models cannot fit the cosmic microwave background (CMB) and other cosmological data. This is, however, based on the assumption of a scale-free spectrum for the primordial density perturbation. An alternative physically motivated form for the spectrum enables a good fit to both SNe Ia (Constitution/Union2) and CMB (WMAP 7-yr) data, and to the locally measured Hubble parameter. Constraints from baryon acoustic oscillations and primordial nucleosynthesis are also satisfied.

Figure 1

The solid (blue) curve shows the primordial power spectrum obtained from a full calculation of the multiple inflation model, with parameters as described in the text. The dashed (red) curve shows the simple parameterization (18), with parameter values ${\mathcal{P}}_0=2.48\times {10}^{-9}$, $a=0.1$, $b=2.0$, $c=3.0$, and $k_0=0.015$. For comparison, the dotted (black) curve shows a standard power-law spectrum with slope $n_s=0.954$, amplitude $A_S=2.3\times {10}^{-9}$, which are the best-fit values for the $\Lambda \mathrm{CDM}$ model with no “running” to the $\mathrm{CMB}+{\mathrm{SN}}_{\mathrm{CfA}}$ data sets (Sec. 6).

Figure 2

The TT and TE power spectra of the models that best fit the CMB and Constitution SNe Ia data. The solid (red) curve is for the void model, calculated using the effective EdS approach described in Sec. 4b, and the dashed (black) curve is for $\Lambda \mathrm{CDM}$. Binned WMAP-7 data is also shown.

Figure 3

Constraints on the effective EdS parameters for the void model with a bump, from CMB and SNe Ia data. The solid (red) contours show the 1 and $2\sigma$ likelihood confidence intervals for the Constitution SNe Ia data set and the dashed (blue) contours are for Union2.

Figure 4

Marginalized 1D likelihoods for the void model with a bump, for the fit to CMB and SNe Ia data. The solid (red) curves are for the Constitution SNe Ia data set and the dashed (blue) curves are for Union2.