Constraining primordial non-Gaussianity via a multitracer technique with surveys by Euclid and the Square Kilometre Array

We forecast future constraints on local-type primordial non-Gaussianity parameter $f_{\mathrm{NL}}$ with a photometric galaxy survey by Euclid, a continuum galaxy survey by Square Kilometre Array (SKA), and their combination. We derive a general expression for the covariance matrix of the power spectrum estimates of multiple tracers to show how the so-called multitracer technique improves constraints on $f_{\mathrm{NL}}$. In particular we clarify the role of the overlap fraction of multiple tracers and the division method of the tracers. Our Fisher matrix analysis indicates that stringent constraints of $\sigma (f_{\mathrm{NL}})\lesssim 1$ can be obtained even with a single survey, assuming five mass bins. When Euclid and SKA phase 1 (2) are combined, constraints on $f_{\mathrm{NL}}$ are improved to $\sigma (f_{\mathrm{NL}})=0.61(0.50)$.

Figure 1

The marginalized error on $f_{\mathrm{NL}}$ as the function of the overlap fraction, for the single redshift bin of $0.7<z<1.2$. Different lines show results with different mass ratio $M_{(2)}/M_{(1)}$.

Figure 2

The marginalized error on $f_{\mathrm{NL}}$ as the function of the number of the tracers in the single redshift bin $0.7<z<1.2$. The mass bins are divided such that they have the equal shot noises.

Figure 3

The marginalized constraint on $f_{\mathrm{NL}}$ as a function of the maximum redshift, assuming the redshift range $0.2<z<z_{\max }$ with width $\mathrm{\Delta }z=0.5$. Here we take five tracers (mass bins) for each redshift bin.

Figure 4

The expected marginalized constraints on $f_{\mathrm{NL}}$ for each survey and combinations.