Constraints on a scale-dependent bias from galaxy clustering

We forecast the future constraints on scale-dependent parametrizations of galaxy bias and their impact on the estimate of cosmological parameters from the power spectrum of galaxies measured in a spectroscopic redshift survey. For the latter we assume a wide survey at relatively large redshifts, similar to the planned Euclid survey, as the baseline for future experiments. To assess the impact of the bias we perform a Fisher matrix analysis, and we adopt two different parametrizations of scale-dependent bias. The fiducial models for galaxy bias are calibrated using mock catalogs of $\mathrm{H}\alpha$ emitting galaxies mimicking the expected properties of the objects that will be targeted by the Euclid survey. In our analysis we have obtained two main results. First of all, allowing for a scale-dependent bias does not significantly increase the errors on the other cosmological parameters apart from the rms amplitude of density fluctuations, ${\sigma }_8$, and the growth index $\gamma$, whose uncertainties increase by a factor up to 2, depending on the bias model adopted. Second, we find that the accuracy in the linear bias parameter $b_0$ can be estimated to within 1%–2% at various redshifts regardless of the fiducial model. The nonlinear bias parameters have significantly large errors that depend on the model adopted. Despite this, in the more realistic scenarios departures from the simple linear bias prescription can be detected with a $\sim 2\sigma$ significance at each redshift explored. Finally, we use the Fisher matrix formalism to assess the impact od assuming an incorrect bias model and find that the systematic errors induced on the cosmological parameters are similar or even larger than the statistical ones.

Figure 1

The 68% probability contours for ${\sigma }_8$ and $\gamma$. Black continuous line: standard scale-independent case, i.e. $n=0$. Red dotted line: FM1-PL with $n=1$. Cyan continuous line: FM1-Q. Blue dot-dashed line: FM2-PL with $n=1$. Green dashed line: FM2-Q.

Figure 2

The 68% probability contours for the parameters $b_0$ and $b_1$ of the FM1-PL model. The dotted red line is the case with $n=1$ while the dashed line in blue shows the case $n=2$. The redshift bins are $z=0.6$, 1.8, 2.0, from inside out.

Figure 3

Contours plots for 68% probability contours for the parameters $A$ and $Q$ of the FM1-Q model. We decided to plot only the bins $z=0.6$, 0.8, 1.6, 1.8, 2.0, from inside out, to improve clarity.

Figure 4

The 68% probability contours for the parameters $b_0$ and $b_1$ of the FM2-PL model for different values of $n$. They are centered at the $b_0$ and $b_1$ values indicated in Table 3. Ellipses of increasing redshifts are centered at increasing values of $b_0$. In the left upper panel we show the case $n=1$. In the right panel we show the $n=1.28$ case. In the lower left panel we show the $n=2$ case. Only the redshifts $z=0.8$, 1.2, 1.6, 1.8 are shown to avoid overcrowding.

Figure 5

The 68% probability contours for the parameters $A$ and $Q$ of the FM2-Q model. We plot only the redshifts $z=0.8$, 1.2, 1.6, 1.8, left to right, to avoid overlaps.