Constraints on Primordial Non-Gaussianity from $800000$ Photometric Quasars

We derive robust constraints on primordial non-Gaussianity (PNG) using the clustering of 800 000 photometric quasars from the Sloan Digital Sky Survey in the redshift range $0.5<z<3.5$. These measurements rely on the novel technique of extended mode projection to control the impact of spatially varying systematics in a robust fashion, making use of blind analysis techniques. This allows the accurate measurement of quasar halo bias at the largest scales, while discarding as little as possible of the data. The standard local-type PNG parameters $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ both imprint a $k^{-2}$ scale-dependent effect in the bias. Constraining these individually, we obtain $-49<f_{\mathrm{NL}}<31$ and $-2.7\times 10^5<g_{\mathrm{NL}}<1.9\times 10^5$, while their joint constraints lead to $-105<f_{\mathrm{NL}}<72$ and $-4.0\times 10^5<g_{\mathrm{NL}}<4.9\times 10^5$ (all at 95% C.L.). Introducing a running parameter $n_{f_{\mathrm{NL}}}$ to constrain $b(k)\propto k^{-2+n_{f_{\mathrm{NL}}}}$ and a generalized PNG amplitude ${\tilde{f}}_{\mathrm{NL}}$, we obtain $-45.5\exp (3.7n_{f_{\mathrm{NL}}})<{\tilde{f}}_{\mathrm{NL}}<34.4\exp (3.3n_{f_{\mathrm{NL}}})$ at 95% C.L. These results incorporate uncertainties in the cosmological parameters, redshift distributions, shot noise, and the bias prescription used to relate the quasar clustering to the underlying dark matter. These are the strongest constraints obtained to date on PNG using a single population of large-scale structure tracers, and are already at the level of pre-Planck constraints from the cosmic microwave background. A conservative forecast for a Large Synoptic Survey Telescope (LSST)-like survey incorporating mode projection yields $\sigma (f_{\mathrm{NL}})\sim 5$—competitive with the Planck result—highlighting the power of upcoming large scale structure surveys to probe the initial conditions of the Universe.

Figure 1

Redshift distributions of the four quasar samples used in this analysis, parametrized as superpositions of normal distributions. The shaded regions show the 1, 2, and $3\sigma$ regions explored when adding 5% uncertainty to the parameters of these fits, which are included in the MCMC analysis.

Figure 2

Constraints on the quasar bias model described in Eq. (4). The solid line shows the fiducial model with $b_0=1$, $\beta =5$, and the shaded bands show the $1\sigma$ constraints ($b_0=0.96\pm 0.15$, 68% C.L., $\beta$ and $f_{\mathrm{NL}}$ marginalized) from the XDQSOz power spectra when varying the bias and PNG parameters, the shot noise, and the redshift distributions. The colored bands show the results when fixing $\beta =5$ and allowing a different bias amplitude in each redshift bin to demonstrate the ability of the overall model to simultaneously describe the four samples.

Figure 3

Constraints on local-type $f_{\mathrm{NL}}$ (in the $\mathrm{\Lambda }\mathrm{CDM}+f_{\mathrm{NL}}$ model, with $n_{f_{\mathrm{NL}}}=g_{\mathrm{NL}}=0$) using the power spectrum analysis of XDQSOz quasars, for different bias models and incorporating uncertainties in the redshift distributions and cosmological parameters. The error bars show the 1 and $2\sigma$ constraints, the dashed line shows $f_{\mathrm{NL}}=0$, and the shaded bands show the constraints from Planck [13].

Figure 4

$1\sigma$ and $2\sigma$ joint constraints on $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ for the $(b_0,\beta )+n(z)+\text{cosmo}$ case, i.e., marginalizing over the uncertainties in the cosmological parameters, redshift distributions, and bias model.

Figure 5

$1\sigma$ and $2\sigma$ joint constraints on ${\tilde{f}}_{\mathrm{NL}}$ and $n_{f_{\mathrm{NL}}}$ for the extended model of Eq. (3), marginalizing over the same parameters as Fig. 4.