Lensing convergence and the neutrino mass scale in galaxy redshift surveys

We demonstrate the importance of including the lensing contribution in galaxy clustering analyses with large galaxy redshift surveys. It is well known that radial cross-correlations between different redshift bins of galaxy surveys are dominated by lensing. But we show here that also neglecting lensing in the autocorrelations within one bin severely biases cosmological parameter estimation with redshift surveys. It leads to significant shifts for several cosmological parameters, most notably the scalar spectral index and the neutrino mass scale. Especially the latter parameter is one of the main targets of future galaxy surveys.

Figure 1

Two- and 1-D posteriors for the cosmological parameters inferred from the full analysis including lensing (red dotted), an analysis neglecting lensing (blue dashed) and considering only auto-correlations (gray solid). The 68% and 95% confidence intervals are shown. Intersections between vertical and horizontal lines denote the fiducial cosmology. In this analysis no significant priors were imposed on the parameters. Circles and squares represent the estimates for the best fits from a Fisher matrix analysis when neglecting lensing, and for the only auto-correlations case, respectively.

Figure 2

The thick red and the thin blue lines correspond to the spectra at the best-fit values estimated by consistently including lensing and by neglecting it, respectively. Gaussian error bars accounting for cosmic variance and shot noise for the consistent analysis are shown as gray regions. The indices for the correlated redshift bins are shown in the legend. The model neglecting lensing cannot fit the data, especially due to redshift cross-correlations.

Figure 3

2D and 1D posteriors for the cosmological parameters inferred from the Fisher analysis excluding (orange solid) and including (red dotted) lensing. We stress that, in the former case, to compute error ellipses within the Fisher formalism, we forecast parameter constraints in a universe where lensing is absent (see the text for more details). The 68% and 95% confidence intervals are shown. Intersections of dashed lines denote the fiducial cosmology. The expected systematic shifts in the best fit due to neglecting lensing in the theoretical modeling are shown, including all bin correlations (circles) and including only autocorrelations (squares). For comparison, we also show the corresponding results from the MCMC analysis. While the Fisher formalism is reliable for a qualitative understanding of parameter degeneracies, the systematic errors are seriously misestimated. See Table 2 for more details about statistical quantities.

Figure 4

2D and 1D posteriors for the cosmological parameters inferred using Planck priors. We show the full analysis including lensing (red dotted), an analysis neglecting lensing (blue dashed), and considering only autocorrelations (gray solid). The 68% and 95% confidence intervals are shown. Intersections between vertical and horizontal lines denote the fiducial cosmology. See Table 3 for numerical values of the statistical quantities.

Figure 5

Euclid photometric galaxy density distribution (black line) with a division into five bins containing the same number of galaxies.

Figure 6

Galaxy bias $b_G(z)$ and magnification bias $s(z)$ for Euclid. The magnification bias is computed at the limiting magnitude $m_{\lim }=24.5$. As a reference, we also plot the value $s=0.4$ at which the lensing contribution to number counts changes sign.