Reconstructing cosmic growth with kinetic Sunyaev-Zel’dovich observations in the era of stage IV experiments

Future ground-based cosmic microwave background (CMB) experiments will generate competitive large-scale structure data sets by precisely characterizing CMB secondary anisotropies over a large fraction of the sky. We describe a method for constraining the growth rate of structure to sub-1% precision out to $z\approx 1$, using a combination of galaxy cluster peculiar velocities measured using the kinetic Sunyaev-Zel’dovich (kSZ) effect, and the velocity field reconstructed from galaxy redshift surveys. We consider only thermal SZ-selected cluster samples, which will consist of $\mathcal{O}(10^4–10^5)$ sources for Stage 3 and 4 CMB experiments respectively. Three different methods for separating the kSZ effect from the primary CMB are compared, including a novel blind “constrained realization” method that improves signal-to-noise by a factor of $\sim 2$ over a commonly-used aperture photometry technique. Assuming a correlation between the integrated tSZ $y$-parameter and the cluster optical depth, it should then be possible to break the kSZ velocity-optical depth degeneracy. The effects of including CMB polarization and SZ profile uncertainties are also considered. In the absence of systematics, a combination of future Stage 4 experiments should be able to measure the product of the growth and expansion rates, $\alpha \equiv fH$, to better than 1% in bins of $\mathrm{\Delta }z=0.1$ out to $z\approx 1$—competitive with contemporary redshift-space distortion constraints from galaxy surveys. We conclude with a discussion of the likely impact of various systematics.

Figure 1

Relative bias (solid lines) and standard deviation (dashed lines) of the reconstructed halo velocities for different Gaussian smoothing scales, in three mass bins at $z=0.3$.

Figure 2

Expected mass and redshift distributions for tSZ-selected clusters detected with the S3 (left) and S4 (right) experiments.

Figure 3

Projected mass (top) and redshift (bottom) distributions of tSZ-selected clusters for S3 (red) and S4 (blue).

Figure 4

Signal-to-noise ratios for the 3 different kSZ measurement methods, as a function of cluster redshift and mass.

Figure 5

Improvement in the kSZ measurement error for S3 after including polarization data. The marginal improvement for large clusters is due to the nonzero correlation between $T$ and $E$, and is negligible overall.

Figure 6

kSZ signal-to-noise ratio for a cluster with mass $M_{500}=3\times 10^{14}{h}^{-1}{M}_{\odot }$ and radial velocity $v_r=300\mathrm{km}/\mathrm{s}$ for S4 with two different beam FWHM: 3 arcminutes (solid lines) and 1 arcminute (dotted lines). The uncertainties for the matched filter approach improve by a factor $\sim 3$ at all redshifts, while the improvement for constrained realizations and AP filtering improves gradually at higher redshifts, due to the smaller effective angle subtended by the cluster.

Figure 7

Forecast constraints on $\alpha \sim fH$ for S3 (dashed lines) and S4 (solid), for the three different methods: matched filtering (MF; red), constrained realizations (CR; gray), and aperture photometry (AP; blue). The redshift bin widths are $\mathrm{\Delta }z=0.2$, 0.1 for S3 and S4 respectively, and we assume full redshift and area overlap with a spectroscopic survey.

Figure 8

Forecast constraints on $\alpha \sim fH$ for S3 and S4 (using the matched filter method), when three different galaxy surveys are used to provide the reconstructed velocity field. Results for an ideal (perfectly overlapping, sample variance-limited) survey are shown in red (cf. Fig. 7). Projected constraints on $\alpha$ from $\mathrm{BAO}+\mathrm{RSDs}$ with a Euclid-like spectroscopic galaxy redshift survey are shown in black.

Figure 9

The tSZ (solid lines) and kSZ (dashed) profiles for clusters with halo masses $2\times 10^{13}{h}^{-1}{M}_{\odot }$ (blue) and $2\times 10^{14}{h}^{-1}{M}_{\odot }$ (red), both at $z=0.3$ with a radial velocity $v_r=-400\mathrm{km}/\mathrm{s}$. The masses are chosen to be broadly representative of the S4 and S3 samples respectively (see Fig. 3). The vertical lines show the characteristic angular scale ${\theta }_{500}$ (solid), and the disc radius ${\theta }_R$ (dotted) for the AP filter for a Stage 3 experiment (1.4 arcmin beam), defined in Sec. 2a2.