Effects of voids on the reconstruction of the equation of state of dark energy

We quantify the effects of the voids known to exist in the Universe upon the reconstruction of the dark energy equation of state $w$. We show that the effect can start to be comparable with some of the other errors taken into account when analyzing supernova data, depending strongly upon the low redshift cutoff used in the sample. For the supernova data alone, the error induced in the reconstruction of $w$ is much larger than the percent level. When the Baryonic Acoustic Oscillations and the Cosmic Microwave Background data are included in the fit, the effect of the voids upon the determination of $w$ is much lessened but is not much smaller than some of the other errors taken into consideration when performing such fits. We also look at the effect of voids upon the estimation of the equation of state when we allow $w$ to vary over time and show that even when supernova, Cosmic Microwave Background, and Baryonic Acoustic Oscillations data are used to constrain the equation of state, the best fit points in parameter space can change at the 10% level due to the presence of voids, and error-bars increase significantly.

Figure 1

Initial density profile define at $t=t_{\mathrm{LTB}}$ and showing the shape of the cosmological voids and of its surrounding walls of denser matter.

Figure 2

Illustration of the binning process allowing us to deal with the statistical nature of our results. The width of each bin is fixed in redshift, $\Delta z=0.01$.

Figure 3

${\Omega }_M$ vs dark energy equation of state $w$ when fitting the Union2 data set only assuming a flat Universe. The shading represents probability from the ${\chi }^2$ cumulative distribution function.

Figure 4

${\Omega }_M$ vs dark energy equation of state $w$ when fitting the Union2 data set, Baryon Acoustic Oscillations, and the shift parameter and acoustic scale of the CMB, again assuming a flat Universe. The shading represents probability from the ${\chi }^2$ cumulative distribution function.

Figure 5

Dark energy equation of state parameters $w_0$ versus $w_a$, with $z_{\min }=0.01$, 0.02, 0.03, and 0.04, respectively, when fitting the Union2 data set, Baryon Acoustic Oscillations, and the shift parameter and acoustic scale of the CMB, always assuming a flat Universe. The contours correspond to the probabilities listed in the individual graph titles.