Improved Modeling of the Kinematic Sunyaev-Zel'dovich Projected-Fields signal and its Cosmological Dependence

Over the past decade, the kinematic Sunyaev-Zel'dovich (kSZ) effect has emerged as an observational probe of the distribution of baryons and velocity fields in the late Universe. Of the many ways to detect the kSZ, the 'projected-fields kSZ estimator' has the promising feature of not being limited to galaxy samples with accurate redshifts. The current theoretical modeling of this estimator involves an approximate treatment only applicable at small scales. As the measurement fidelity rapidly improves, we find it necessary to move beyond the original treatment and hence derive an improved theoretical model for this estimator without these previous approximations. We show that the differences between the predicted signal from the two models are scale-dependent and will be significant for future measurements from the Simons Observatory and CMB-S4 in combination with galaxy data from WISE or the Rubin Observatory, which have high forecasted signal-to-noise ratios ($>100$). Thus, adopting our improved model in future analyses will be important to avoid biases. Equipped with our model, we explore the cosmological dependence of this kSZ signal for future measurements. With a Planck prior, residual uncertainty on $\Lambda$CDM parameters leads to $\sim7\%$ marginalized uncertainties on the signal amplitude, compared to a sub-percent level forecasted with a fixed cosmology. To illustrate the potential of this kSZ estimator as a cosmological probe, we forecast initial constraints on $\Lambda$CDM parameters and the sum of neutrino masses, paving the way for jointly fitting both baryonic astrophysics and cosmology in future analyses.