We investigate the dependence of cosmological parameters on the number count of peaks ( local maxima and minima ) in the cosmic microwave background ( CMB ) sky .
The peak statistics contains the whole information of acoustic oscillations in the angular power spectrum C _ { l } over l -space and thus it can place complementary constraints on the cosmological parameters to those obtained from measurements of C _ { l } .
Based on the instrumental specifications of Planck , we find that the number count of peaks can provide new constraints on the combination of the matter density \Omega _ { m } and the Hubble parameter h approximately scaled as \Omega _ { m } h ^ { -4.9 } for a flat \Lambda CDM model with \Omega _ { m } = 0.3 and h = 0.7 .
Therefore , we suggest that combining it with the constraints from C _ { l } scaled as \Omega _ { m } h ^ { 3.8 } ( or commonly \Omega _ { m } h ^ { 2 } ) can potentially determine \Omega _ { m } or equivalently solve the cosmic degeneracy by the CMB data alone .