The power spectrum and bispectrum of SDSS DR11 BOSS galaxies II:
  cosmological interpretation
  We examine the cosmological implications of the measurements of the linear
growth rate of cosmological structure obtained in a companion paper from the
power spectrum and bispectrum monopoles of the Sloan Digital Sky Survey III
Baryon Oscillation Spectroscopic Survey Data, Release 11, CMASS galaxies. This
measurement was of $f^{0.43}\sigma_8$, where $\sigma_8$ is the amplitude of
dark matter density fluctuations, and $f$ is the linear growth rate, at the
effective redshift of the survey, $z_{\rm eff}=0.57$. In conjunction with
Cosmic Microwave Background (CMB) data, interesting constraints can be placed
on models with non-standard neutrino properties and models where gravity
deviates from general relativity on cosmological scales. In particular, the sum
of the masses of the three species of the neutrinos is constrained to
$m_\nu<0.49\,{\rm eV}$ (at 95\% confidence level) when the $f^{0.43}\sigma_8$
measurement is combined with state-of-the-art CMB measurements. Allowing the
effective number of neutrinos to vary as a free parameter does not
significantly change these results. When we combine the measurement of
$f^{0.43}\sigma_8$ with the complementary measurement of $f\sigma_8$ from the
monopole and quadrupole of the two-point correlation function we are able to
obtain an independent measurements of $f$ and $\sigma_8$. We obtain
$f=0.63\pm0.16$ and $\sigma_8=0.710\pm0.086$ (68\% confidence level). This is
the first time when these parameters have been able to be measured
independently using the redshift-space power spectrum and bispectrum
measurements from galaxy clustering data only.
