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We use the number density of peaks in the smoothed cosmological density field taken from the 2dF Galaxy Redshift Survey to constrain parameters related to the power spectrum of mass fluctuations,  n  (the spectral index),  d n /d ln  k   (rolling in the spectral index) and the neutrino mass,   m  ν  . In a companion paper we use  N ‐body simulations to study how the peak density responds to changes in the power spectrum, the presence of redshift distortions and the relationship between galaxies and dark matter haloes. In the present paper we make measurements of the peak density from 2dF Galaxy Redshift Survey data, for a range of smoothing filter scales from 4 to  33  h  −1  Mpc . We use these measurements to constrain the cosmological parameters, finding   n = 1.36 +0.75  −0.64 ,  m  ν  &lt; 1.76 eV, d n /d ln  k =−0.012 +0.192  −0.208  , at the 68 per cent confidence level, where   m  ν   is the total mass of three massive neutrinos. At 95 per cent confidence we find   m  ν  &lt; 2.48 eV . These measurements represent an alternative way to constrain cosmological parameters to the usual direct fits to the galaxy power spectrum, and are expected to be relatively insensitive to non‐linear clustering evolution and galaxy biasing.

Peaks in the cosmological density field: parameter constraints from 2dF Galaxy Redshift Survey data