The kinematic Sunyaev-Zel'dovich effect of the large-scale structure (II): the effect of modified gravity
The key to understand the nature of dark energy relies in our ability to probe the distant Universe. In this framework, the recent detection of the kinematic Sunyaev-Zel'dovich (kSZ) effect signature in the cosmic microwave background obtained with the South Pole Telescope (SPT) is extremely useful since this observable is sensitive to the high-redshift diffuse plasma. We analyse a set of cosmological hydrodynamical simulation with 4 different realisations of a Hu & Sawicki $f(R)$ gravity model, parametrised by the values of $\overline{f}_{\rm R,0}=(0,-10^{-6},-10^{-5},-10^{-4})$, to compute the properties of the kSZ effect due to the ionized Universe and how they depend on $\overline{f}_{\rm R,0}$ and on the redshift of reionization, $z_{\rm re}$. In the standard General Relativity limit ($\overline{f}_{\rm R,0}$=0) we obtain an amplitude of the kSZ power spectrum of $\mathcal{D}^{\rm kSZ}_{3000}=4.1\,$$μ$K$^2$ ($z_{\rm re}$=8.8), close to the $+1σ$ limit of the $\mathcal{D}^{\rm kSZ}_{3000}=(2.9\pm1.3)\,$$μ$K$^2$ measurement by SPT. This corresponds to an upper limit on the kSZ contribute from patchy reionization of $\mathcal{D}^{\rm kSZ,patchy}_{3000}<0.9\,$$μ$K$^2$ (95 per cent confidence level). Modified gravity boosts the kSZ signal by about 3, 12 and 50 per cent for $\overline{f}_{\rm R,0}=(-10^{-6},-10^{-5},-10^{-4})$, respectively, with almost no dependence on the angular scale. This means that with modified gravity the limits on patchy reionization shrink significantly: for $\overline{f}_{\rm R,0}=-10^{-5}$ we obtain $\mathcal{D}^{\rm kSZ,patchy}_{3000}<0.4\,$$μ$K$^2$. Finally, we provide an analytical formula for the scaling of the kSZ power spectrum with $z_{\rm re}$ and $\overline{f}_{\rm R,0}$ at different multipoles: at $\ell=3000$ we obtain $\mathcal{D}^{\rm kSZ}_{3000}\propto z_{\rm re}^{0.24}\left(1+\sqrt{\left|\overline{f}_{\rm R,0}\right|}\right)^{41}$.