  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), dn/d(lnk)
(rolling in the spectral index), and the neutrino mass, m_nu. 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 halos. 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 4-33 h^-1 Mpc. We use these
measurements to constrain the cosmological parameters, finding n=1.36
(+0.75)(-0.64), m_nu < 1.76 eV, dn/d(lnk)=-0.012 (+0.192)(-0.208), at the 68 %
confidence level, where m_nu is the total mass of three massive neutrinos. At
95% confidence we find m_nu< 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.
