The kSZ optical depth degeneracy and future constraints on local primordial non-Gaussianity

TL;DR

This paper assesses how recent measurements indicating a suppressed small-scale galaxy–electron cross power $P_{ge}$, quantified by a low kSZ velocity bias $b_v$, affect forecasts for local primordial non-Gaussianity $f_{NL}^{\rm loc}$ from kSZ tomography. Using simple, tunable models for $P_{ge}$ suppression and a Fisher-matrix framework, the authors forecast LSST-like galaxy data (with and without SPHEREx) combined with CMB measurements, exploring how high-redshift ($z\gtrsim 1$) small-scale power impacts velocity reconstruction noise and the scale-dependent bias signal. They find that if the suppression persists to higher redshifts, the expected improvements in $\sigma(f_{NL}^{\rm loc})$ from kSZ tomography can be substantially weaker (roughly 30–40% degradation) than forecasts based on fiducial AGN-like $P_{ge}$ models; conversely, if suppression is limited to low redshift, gains remain robust. The work highlights the critical role of high-$z$ velocity-reconstruction physics for LPnG constraints and motivates further modeling and high-redshift velocity measurements to calibrate the kSZ program's cosmological utility.

Abstract

Recent reconstructions of the large-scale cosmological velocity field with kinetic Sunyaev Zeldovich (kSZ) tomography have returned an amplitude that is low with respect to the halo model prediction, captured by the kSZ velocity reconstruction bias $b_v <1$. This suggests that common choices for modeling the galaxy-electron cross correlation have systematically overestimated the true power, at least over scales and redshifts used in the velocity reconstruction measurements. In this paper, we study the implications of this overestimation for constraints on local-type primordial non-Gaussianity in current and near-future cosmological surveys. For concreteness, we focus on kSZ velocity reconstruction from a Vera Rubin Observatory-like survey in tandem with contemporary cosmic microwave background measurements. Assuming standard choices for the fiducial model of the small-scale galaxy-electron cross correlation, we find that upcoming kSZ tomography measurements can significantly improve constraints on local primordial non-Gaussianity via measurement of scale-dependent galaxy bias, in broad concordance with previous studies of the application of kSZ tomography to primordial non-Gaussianity. However, when we instead modify the assumed galaxy-electron cross-spectrum to be consistent with recent measurements of the velocity reconstruction bias, this picture can change appreciably. Specifically, we find that if the inferred suppression of galaxy-electron power persists at higher redshifts $z\gtrsim 1$, kSZ-driven improvement in local primordial non-Gaussianity constraints may be less significant than previously estimated. We explore how these conclusions depend on various modeling and experimental assumptions and discuss implications for the emerging program of kSZ velocity reconstruction.

Figures (4)

• Figure 1: Comparing galaxy-electron power spectra models (upper panel) and their corresponding effect on the $b_v$ integrand (lower panel) at $z=0.7$. The AGN model (blue line) is compared to a flat suppression (orange line), Eq. (\ref{['eq:Pge_suppress_models_flat']}), and an exponential suppression (green line), Eq. (\ref{['eq:Pge_suppress_models_roll']}). As detailed in the main body of the text, the model parameters of the suppressed orange and green curves, $A^2=0.45$ and $k_* = 2.38 / \rm{Mpc}$ respectively, are chosen to reproduce the value of $b_v=0.45$ of Ref. Hotinli:2025tul (with respect to the AGN model, hence the blue curve has $b_v=1$ by definition), when approximating their CMB and galaxy survey details. Note the upper and lower panels share a legend and a horizontal axis.
• Figure 2: The kSZ velocity reconstruction noise (upper panels), modulated by a factor $(k/faH)^2$ to correspond to the reconstruction noise on the density modes Smith:2018bpnMunchmeyer:2018eey, for varying $P_{ge}$ models, and the ratio of these reconstruction noises to that obtained from the AGN model (lower panel), for three redshifts $z\in[0.3,0.7,2.5]$ (left, center, and right panels respectively), for purely radial modes $\mu=-1$. The flat suppression model (orange, Eq. (\ref{['eq:Pge_suppress_models_flat']})) and exponential suppression models (Eq. (\ref{['eq:Pge_suppress_models_roll']}), green solid and dot-dashed) yield a larger reconstruction noise than the AGN model (blue). The model parameters $(A,k_*,z_*)$ are the same as in Fig. \ref{['fig:Nv_Pge_compare']}, as described in the main body of the text. Note the solid and dot-dashed green curves lie exactly on top of one another in the center panel. Here, the CMB experiment is assumed to have a $1.4'$ resolution and noise level $\Delta_T = 4 \mu K'$, and the galaxy survey specifications are that of our LSSTY10 forcast, outlined further in Sec. \ref{['subsec:surveys']} and Table \ref{['tab:LSST']}.
• Figure 3: Constraints on $\sigma(f_{NL}^{\rm{loc}})$ from galaxy tomography (gray, dashed lines) and the combination of galaxy and kSZ tomography (solid and dot-dashed lines, in color) from LSST (left panel) and LSST+SPHEREx (right panel) as a function of varying CMB noise $\Delta_T$. The blue curves assume the standard AGN model. The orange lines use a flat suppression of the AGN model, Eq. (\ref{['eq:Pge_suppress_models_flat']}), with a suppression factor $A^2(z<1)=0.45, A^2(z>1)=1$ (solid), and $A^2 = 0.45$ for all $z$ (dot-dashed) respectively. The green curves use an exponential suppression of the AGN model on small scales, Eq.( \ref{['eq:Pge_suppress_models_roll']}), with a fixed comoving suppression scale $k_* = 2.38 \, \rm{Mpc}^{-1}$ (solid) and a redshift dependent one, $k_*(z) = k_{z_*}(1+z_*)/(1+z)$ (dot-dashed), with $z_* =0.7, k_{z_*} = 2.38\,\rm{Mpc}^{-1}$. Per the main body of the text, the constants $A,k_*$, etc. are chosen to reproduce the value of $b_v = 0.45$ with respect to the AGN model.
• Figure 4: Impact of large-scale modes (i.e., $k_{\rm{min}}$) on $\sigma(f_{NL}^{\rm{loc}})$ from galaxy tomography (dashed lines) and the combination of galaxy and kSZ tomography (solid lines), assuming an LSST-like survey (Table \ref{['tab:LSST']}). Our fiducial results for the galaxy power spectrum alone and the combination of galaxy and kSZ tomography (assuming the AGN model), with $k_{\rm{min}} =\pi/V^{1/3}(z)$, are shown again in dashed gray and solid blue, respectively. The impact on these constraints from removing large-scale information, by doubling the minimum wavenumber in the Fisher matrix, is shown in black dashed (galaxies alone) and solid purple (galaxies and kSZ) respectively.