Designing an Inflation Galaxy Survey: how to measure $σ(f_{\rm NL}) \sim 1$ using scale-dependent galaxy bias

Abstract: The most promising method for measuring primordial non-Gaussianity in the post-Planck era is to detect large-scale, scale-dependent galaxy bias. Considering the information in the galaxy power spectrum, we here derive the properties of a galaxy clustering survey that would optimize constraints on primordial non-Gaussianity using this technique. Specifically, we ask the question what survey design is needed to reach a precision $\sigma(f_{\rm NL}^{\rm loc}) \approx 1$. To answer this question, we calculate the sensitivity to $f_{\rm NL}^{\rm loc}$ as a function of galaxy number density, redshift accuracy and sky coverage. We include the multitracer technique, which helps minimize cosmic variance noise, by considering the possibility of dividing the galaxy sample into stellar mass bins. We show that the ideal survey for $f_{\rm NL}^{\rm loc}$ looks very different than most galaxy redshift surveys scheduled for the near future. Since those are more or less optimized for measuring the BAO scale, they typically require spectroscopic redshifts. On the contrary, to optimize the $f_{\rm NL}^{\rm loc}$ measurement, a deep, wide, multi-band imaging survey is preferred. An uncertainty $\sigma(f_{\rm NL}^{\rm loc}) = 1$ can be reached with a full-sky survey that is complete to an $i$-band AB magnitude $i \approx 23$ and has a number density $\sim 8$ arcmin$^{-2}$. Requirements on the multi-band photometry are set by a modest photo-$z$ accuracy $\sigma(z)/(1+z) < 0.1$ and the ability to measure stellar mass with a precision $\sim 0.2$ dex or better (or another proxy for halo mass with equivalent scatter). While here we focus on the information in the power spectrum, even stronger constraints can potentially be obtained with the galaxy bispectrum.