Constraining local non-Gaussianities with kinetic Sunyaev-Zel’dovich tomography

Kinetic Sunyaev Zel’dovich (kSZ) tomography provides a powerful probe of the radial velocity field of matter in the Universe. By cross-correlating a high resolution cosmic microwave background (CMB) experiment like CMB-S4 and a galaxy survey like Dark Energy Spectroscopic Instrument (DESI) or Large Synoptic Survey Telescope (LSST), one can measure the radial velocity field with a very high signal-to-noise ratio over a large volume of the universe. In this paper we show how this measurement can be used to improve constraints on primordial non-Gaussianities of the local type. The velocity field provides a measurement of the unbiased matter perturbations on large scales, which can be cross-correlated with the biased large-scale galaxy density field. This results in sample variance cancellation for a measurement of scale-dependent bias due to a nonzero $f_{NL}$. Using this method we forecast that CMB-S4 and LSST combined reach a sensitivity ${\sigma }_{f_{NL}}\sim 0.5$, which is a factor of 3 improvement over the sensitivity using LSST alone (without internal sample variance cancellation). We take into account critical systematics like photometric redshifts, the kSZ optical depth degeneracy, and systematics affecting the shape of the galaxy auto-power spectrum and find that these have negligible impact, thus making kSZ tomography a robust probe for primordial non-Gaussianities. We also forecast the impact of mass binning on our constraints. The techniques proposed in this paper could be an important component of achieving the theoretically important threshold of ${\sigma }_{f_{NL}}\lesssim 1$ with future surveys.

Figure 1

Galaxy power spectra and noise power spectra for an experimental configuration corresponding to the DESI experiment (with galaxy density and CMB noise according to our baseline 1 defined in Table 1). At large scales, where the $f_{NL}$ signal is strongest, we get a much lower noise using kSZ tomography than with galaxies alone, due to the $k^2$ scaling of the kSZ reconstruction noise. The chosen $f_{NL}$ value of 5 is near the $1\sigma$ sensitivity for this configuration. All power spectra are shown at $z=1$ and for mu $|\mu |=1$ (radial modes), and the galaxy power spectra include the redshift-space distortions term.

Figure 2

Left: redshift binning and bias as a function of $z$ for the LSST forecast. Right: HOD stellar mass threshold $m_{\star }^{\text{thresh}}$ as a function of $z$ matched so that the galaxy number predicted by the halo model matches Eq. (8), extracted from the LSST science book.

Figure 3

Left: sensitivity ${\sigma }_{f_{NL}}$ as a function of $k_{\min }$ for baseline 2. On the lower end, $k$ is cut off by the size of the volume. The plot illustrates which scales contribute most to the signal. Right: correlation coefficient of velocity and galaxy modes for $\mu =1$ modes, for both baseline configurations. The influence of photo-$z$ errors in baseline 2 is clearly visible at high $k$.

Figure 4

Left: sensitivity ${\sigma }_{f_{NL}}$ as a function of galaxy density $n_{\mathrm{gal}}$ for baseline 2. Galaxy density is a critical parameter for our method, in particular because increasing it improves the shot noise of the galaxy mode for sample variance cancellation. For clarity in this plot we have kept the bias constant; however, of course highly biased galaxies are limited in number. Right: velocity reconstruction noise $N_{vv}$ as a function of galaxy density $n_{\mathrm{gal}}$ for baseline 2. This illustrates that for baseline 2 the galaxy density is so large that with CMB-S4 noise levels we are close to signal-to-noise saturation of the velocity reconstruction as a function of $n_{\mathrm{gal}}$.

Figure 5

Top: sensitivity ${\sigma }_{f_{NL}}$ (left) and velocity reconstruction noise $N_{vv}$ (right) as a function of CMB noise for baseline 2. Bottom: sensitivity ${\sigma }_{f_{NL}}$ (left) and velocity reconstruction noise $N_{vv}$ (right) as a function of CMB beam for baseline 2. For the $f_{NL}$ measurement the CMB noise parameters are less critical than the galaxy density, as long as they suffice to get a velocity reconstruction from the CMB, in which case the velocity reconstruction becomes quickly superior to the shot noise limited galaxy mode measurement.

Figure 6

Constraints ${\sigma }_{f_{NL}}$ (left) and improvement factor (right) as a function of redshift bin (per bin, not cumulative). The total combined sensitivity for $\mathrm{kSZ}+\mathrm{galaxies}$ is ${\sigma }_{f_{NL}}=0.45$, an improvement by a factor of 3.00 with respect to the galaxies alone with ${\sigma }_{f_{NL}}=1.35$. The plot includes LSST gold sample galaxy density, biases and photo-$z$’s, and CMB-S4 noise levels.

Figure 7

Left: constraints ${\sigma }_{f_{NL}}$ for galaxies and for $\mathrm{galaxies}+\mathrm{kSZ}$ as a function of $M_{\min }^{\mathrm{halo}}$ in a multitracer analysis. From left to right on the $x$ axis, each new dot removes one low mass bin from the forecast. For this analysis we used a survey with survey volume $100{\mathrm{Gpc}}^3$ and central redshift $z_{\star }=1$. This forecast uses the halo model number densities $n_h$, biases $b_h$ and power spectra $P_{gg},P_{ge}$. Right: improvement factor due to adding the kSZ information.