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We examine the cosmological implications of the measurements of the lineargrowth rate of cosmological structure obtained in a companion paper from thepower spectrum and bispectrum monopoles of the Sloan Digital Sky Survey IIIBaryon Oscillation Spectroscopic Survey Data, Release 11, CMASS galaxies. Thismeasurement was of $f^{0.43}\sigma_8$, where $\sigma_8$ is the amplitude ofdark matter density fluctuations, and $f$ is the linear growth rate, at theeffective redshift of the survey, $z_{\rm eff}=0.57$. In conjunction withCosmic Microwave Background (CMB) data, interesting constraints can be placedon models with non-standard neutrino properties and models where gravitydeviates from general relativity on cosmological scales. In particular, the sumof 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 theeffective number of neutrinos to vary as a free parameter does notsignificantly change these results. When we combine the measurement of$f^{0.43}\sigma_8$ with the complementary measurement of $f\sigma_8$ from themonopole and quadrupole of the two-point correlation function we are able toobtain 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 isthe first time when these parameters have been able to be measuredindependently using the redshift-space power spectrum and bispectrummeasurements from galaxy clustering data only.

The power spectrum and bispectrum of SDSS DR11 BOSS galaxies II: cosmological interpretation