The impact of nonlinear structure formation on the power spectrum of transverse momentum fluctuations and the kinetic Sunyaev–Zel'dovich effect

Cosmological transverse momentum fields, whose directions are perpendicular to Fourier wave vectors, induce temperature anisotropies in the cosmic microwave background via the kinetic Sunyaev–Zel'dovich (kSZ) effect. The transverse momentum power spectrum contains the four-point function of density and velocity fields, $⟨\delta \delta vv⟩.$ 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 ($k>0.1h{Mpc}^{-1}$) is subdominant relative to the unconnected term, we find that its contribution to the kSZ power spectrum at $\ell =3000$ 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. The power spectrum of transverse momentum on large scales is expected to scale as k² as a consequence of momentum conservation. We show that both the leading and the next-to-leading order terms satisfy this scaling. In particular, we find that both of the unconnected and connected terms are necessary to reproduce k².