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 } _ { 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 } _ { R, 0 } and on the redshift of reionization , z _ { re } .
In the standard General Relativity limit ( \overline { f } _ { R, 0 } =0 ) we obtain an amplitude of the kSZ power spectrum of \mathcal { D } ^ { kSZ } _ { 3000 } = 4.1 \umu K ^ { 2 } ( z _ { re } =8.8 ) , close to the +1 \sigma limit of the \mathcal { D } ^ { kSZ } _ { 3000 } = ( 2.9 \pm 1.3 ) \umu K ^ { 2 } measurement by SPT .
This corresponds to an upper limit on the kSZ contribute from patchy reionization of \mathcal { D } ^ { kSZ,patchy } _ { 3000 } < 0.9 \umu K ^ { 2 } ( 95 per cent confidence level ) .
Modified gravity boosts the kSZ signal by about 3 , 12 and 50 per cent for \overline { f } _ { 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 } _ { R, 0 } = -10 ^ { -5 } we obtain \mathcal { D } ^ { kSZ,patchy } _ { 3000 } < 0.4 \umu K ^ { 2 } .
Finally , we provide an analytical formula for the scaling of the kSZ power spectrum with z _ { re } and \overline { f } _ { R, 0 } at different multipoles : at \ell = 3000 we obtain \mathcal { D } ^ { kSZ } _ { 3000 } \propto z _ { re } ^ { 0.24 } \left ( 1 + \sqrt { \left| \overline { f } _ { R, 0 } \right| } \right ) ^ { 41 } .