The Impact of Nonlinear Structure Formation on the Power Spectrum of Transverse Momentum Fluctuations and the Kinetic Sunyaev-Zel’dovich Effect

Abstract: Cosmological transverse momentum fields, whose directions are perpendicular to Fourier wave vectors, induce temperature anisotropies in the cosmic microwave background via the kinetic Sunyaev-Zeldovich (kSZ) effect. The transverse momentum power spectrum contains the four-point function of density and velocity fields, . In the post-reionization epoch, nonlinear effects dominate in the power spectrum. We use perturbation theory and cosmological N-body simulations to calculate this nonlinearity. We derive the next-to-leading order expression for the power spectrum with a particular emphasis on the connected term that has been ignored in the literature. While the contribution from the connected term on small scales (k>0.1 h/Mpc) is subdominant relative to the unconnected term, we find that its contribution to the kSZ power spectrum at l = 3000 at z<6 can be as large as ten percent of the unconnected term, which would reduce the allowed contribution from the reionization epoch (z>6) by twenty percent.