Large-Scale Inhomogeneities May Improve the Cosmic Concordance of Supernovae

We reanalyze the supernova data from the Union Compilation including the weak-lensing effects caused by inhomogeneities. We compute the lensing probability distribution function for each background solution described by the parameters ${\Omega }_M$, ${\Omega }_{\Lambda }$, and $w$ in the presence of inhomogeneities, approximately modeled with a single-mass population of halos. We then perform a likelihood analysis in the parameter space of Friedmann-Lemaître-Robertson-Walker models and compare our results with the standard approach. We find that the inclusion of lensing can move the best-fit model significantly towards the cosmic concordance of the flat Lambda-Cold Dark Matter model, improving the agreement with the constraints coming from the cosmic microwave background and baryon acoustic oscillations.

Figure 1

PDFs for a SN with $\sigma =0.25$ mag at $z_s=1.5$ in the $\Lambda \mathrm{CDM}$ model endowed with halos specified by $z_{\mathrm{vir}}=0.8$ and ${\lambda }_c=12.6h^{-1}\mathrm{Mpc}$. The dotted histogram represents the lensing PDF, the dashed line the SN PDF and the solid line the full likelihood. The dotted curve is described in the text.

Figure 2

1, 2, and $3\sigma$ confidence level contours on $w$ and ${\Omega }_M$, for a flat $w\mathrm{CDM}$ universe with halos specified by $z_{\mathrm{vir}}=0.8$ and ${\lambda }_c=12.6h^{-1}\mathrm{Mpc}$. The results using the full likelihood of Eq. (5) are shown as filled contours and the best-fit model with a circle. The results using the gaussian $G_i$ are shown as dotted lines with a triangle, the ones using the unlensed $P_{\mathrm{SN}}$ are shown as dashed lines with a square and correspond to the ones of Ref. 5 (without systematics).

Figure 3

1, 2 and $3\sigma$ confidence level contours on ${\Omega }_M$ and ${\Omega }_{\Lambda }$ (i.e., allowing for nonzero curvature) for $\Lambda \mathrm{CDM}$ ($w=-1$) with halos as in Fig. 2. Note that, as also in the previous plot, the new best-fit points lie on the $1\sigma$ confidence level contour relative to $P_{\mathrm{SN}}$. Labeling as in Fig. 2.