Probing primordial non-Gaussianity with SKA galaxy redshift surveys: a fully relativistic analysis

TL;DR

This paper assesses how SKA HI galaxy redshift surveys can constrain primordial non-Gaussianity by performing fully relativistic forecasts of the large-scale galaxy power spectrum. It introduces and incorporates both primordial GR corrections and linear relativistic projection effects, and uses tomographic angular power spectra calculated with camb_sources to obtain Fisher-based constraints on $f_{ m NL}$. The results show that including relativistic corrections is crucial on horizon scales, with full SKA forecasts reaching $\sigma(f_{ m NL})$ around $1.54$ for $0<z\leq3$, and around $3.12$ for $0<z\leq1.5$, beating Planck by factors of several. These findings imply that SKA, especially in its full configuration, can test standard slow-roll single-field inflation and provide a robust, large-volume complement to CMB PNG measurements, while highlighting the importance of modeling magnification and evolution biases as well as GR effects.

Abstract

The Square Kilometre Array (SKA) will produce spectroscopic surveys of tens to hundreds of millions of HI galaxies, eventually covering 30,000 sq. deg. and reaching out to redshift z~2. The huge volumes probed by the SKA will allow for some of the best constraints on primordial non-Gaussianity, based on measurements of the large-scale power spectrum. We investigate various observational set-ups for HI galaxy redshift surveys, compatible with the SKA Phase 1 and Phase 2 (full SKA) configurations. We use the corresponding number counts and bias for each survey from realistic simulations and derive the magnification bias and the evolution of source counts directly from these. For the first time, we produce forecasts that fully include the general relativistic effects on the galaxy number counts. These corrections to the standard analysis become important on very large scales, where the signal of primordial non-Gaussianity grows strongest. Our results show that, for the full survey, the non-Gaussianity parameter fNL can be constrained down to an accuracy of 1.54. This improves the current limit set by the Planck satellite by a factor of five, using a completely different approach.

Figures (5)

• Figure 1: Key functions derived from simulations for SKA HI galaxy redshift surveys, with sensitivities of $3$, $7.3$, $23$, $70$ and $100$$\mu$Jy (black, red, blue, green and magenta curves, respectively). Top:Hi galaxy number distribution per unit redshift per square degree, $\mathrm d n_g/\mathrm d z=a^3N_g(\chi^2/H)(\pi/180)^2$. Second: HI galaxy bias, $b(z)$, for ${f_\mathrm{NL}}=0$. Third: Magnification bias, $\mathcal{Q}(z)$. Bottom: Evolution bias, $b_e(z)$. [ Note: in the published version (arXiv v4), there are errors in the $\mathcal{Q}$ and $b_e$ plots, which have been corrected here.]
• Figure 2: Forecast 68$\%$ errors on ${f_\mathrm{NL}}$ marginalised over $\sigma_8$ for $0<z\leq 1.5$. Left: As a function of flux cut for ${\ell_{\rm min}}=2$ and ${\ell_{\rm max}}=700$. The dotted horizontal line shows the current Planck constraint (in the LSS convention). Right: As a function of ${\ell_{\rm min}}$ and for various flux cuts and two values of ${\ell_{\rm max}}$.
• Figure 3: Marginal 1$\sigma$ error contours in the $\sigma_8$--${f_\mathrm{NL}}$ plane at 3$\,\mu$Jy sensitivity for the three redshift chunks and their combination.
• Figure 4: Ratio of the angular power spectrum to the fiducial one for the third redshift slice of the 3 $\mu$Jy case when ${f_\mathrm{NL}}$ and $\mathcal{Q}$ are changed.
• Figure 5: Background galaxy number density with flux larger than the flux threshold for $z=0.1$, $0.3$, $0.6$, $0.9$, $1.2$ and $1.5$ from top (right) to bottom. Solid lines are the outcome of Eq. \ref{['eq:fit']}, bullets come from the tables in Yahya:2014yva. [ Note: This corrects errors in the published version (arXiv v4).]