An analysis of the physics-rich endgame of reionization at z = 5.7 is performed , utilizing jointly the observations of the Ly \alpha forest , the mean free path of ionizing photons , the luminosity function of galaxies and new physical insight .
We find that an upper limit on { \tau _ { e } } provides a constraint on the minimum mean free path ( of ionizing photons ) that is primarily due to dwarf galaxies , which in turn yields a new and yet the strongest constraint on the matter power spectrum on 10 ^ { 6 } -10 ^ { 9 } { M _ { \odot } } scales .
With the latest Planck measurements of { \tau _ { e } = 0.055 \pm 0.009 } , we can place an upper limit of ( 8.9 \times 10 ^ { 6 } , 3.8 \times 10 ^ { 7 } , 4.2 \times 10 ^ { 8 } ) { M _ { \odot } } on the lower cutoff mass of the halo mass function , or equivalent a lower limit on warm dark matter particle mass { m _ { x } \geq ( 15.1 , 9.8 , 4.6 ) keV } or on sterile neutrino mass { m _ { s } \geq ( 161 , 90 , 33 ) keV } , at ( 1 , 1.4 , 2.2 ) \sigma confidence level , respectively .