Living in a Void: Testing the Copernican Principle with Distant Supernovae

We show that the local redshift dependence of the luminosity distance can be used to test the Copernican principle that we are not in a central or otherwise special region of the Universe. Future surveys of type Ia supernovae that focus on a redshift range of $\sim 0.1–0.4$ will be ideally suited to observationally determine the validity of the Copernican principle on new scales, as well as probing the degree to which dark energy must be considered a necessary ingredient in the Universe.

Figure 1

Some representative forms for the curvature function $k(r)$ and the corresponding distance moduli, normalized to an empty Milne cosmology $\Delta dm$. Void (a) is a Gaussian in $r$ (with FWHM $r_0$), void (b) is a $k\propto \exp \{-c|r{|}^3\}$, and void (c) is $k\propto \{1-|\tanh (r)|\}$, all normalized to the curvature minimum $k_0$. The three diagrams on top indicate the spatial distribution of energy density in the three voids at some sample time [the solid line for void (a), the dashed line for void (b), and the dotted line for void (c)]. The ascending thick solid line on the right-hand plot corresponds to a universe containing dark energy only (de Sitter space) and the descending one to a flat universe containing only dust (an Einstein–de Sitter universe).

Figure 2

The current best fit $\Lambda \mathrm{CDM}$ and Gaussian void models as dashed and solid lines, with triangular and square data points, respectively. The data shown here is a compilation of 115 low- and high-$z$ SNe from the SNLS, fitted using SALT [20]. For illustrative purposes we have binned the results with 10 SNe per bin (except the last one, which contains 5). Because of the uncertainty in the nuisance parameters of the calibration, the data points and the error bars shift when fitting for different models.

Figure 3

The best fit $\Lambda \mathrm{CDM}$ and Gaussian void models as dashed and solid lines, with triangular and square data points, respectively, for an example of 700 SNe simulated from a $\Lambda \mathrm{CDM}$ model using the SALT light-curve fitter. The shape of the redshift distribution used here is similar to that expected from the 2000 JDEM SNe, with an extra 300 at low $z$. We find that 700 SNe, with this redshift distribution, can decisively recover the $\Lambda \mathrm{CDM}$ model 99% of the time, as it becomes evident that a void model cannot mimic the low redshift behavior of a $\Lambda \mathrm{CDM}$ cosmology. For illustrative purposes, we have binned in groups of 60.