The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the power spectrum and bispectrum of the DR12 BOSS galaxies

We measure and analyse the bispectrum of the final, Data Release 12, galaxy sample provided by the Baryon Oscillation Spectroscopic Survey, splitting by selection algorithm into LOWZ and CMASS galaxies. The LOWZ sample contains 361\,762 galaxies with an effective redshift of $z_{\rm LOWZ}=0.32$, and the CMASS sample 777\,202 galaxies with an effective redshift of $z_{\rm CMASS}=0.57$. Combining the power spectrum, measured relative to the line-of-sight, with the spherically averaged bispectrum, we are able to constrain the product of the growth of structure parameter, $f$, and the amplitude of dark matter density fluctuations, $σ_8$, along with the geometric Alcock-Paczynski parameters, the product of the Hubble constant and the comoving sound horizon at the baryon drag epoch, $H(z)r_s(z_d)$, and the angular distance parameter divided by the sound horizon, $D_A(z)/r_s(z_d)$. After combining pre-reconstruction RSD analyses of the power spectrum monopole, quadrupole and bispectrum monopole; with post-reconstruction analysis of the BAO power spectrum monopole and quadrupole, we find $f(z_{\rm LOWZ})σ_8(z_{\rm LOWZ})=0.427\pm 0.056$, $D_A(z_{\rm LOWZ})/r_s(z_d)=6.60 \pm 0.13$, $H(z_{\rm LOWZ})r_s(z_d)=(11.55\pm 0.38)10^3\,{\rm kms}^{-1}$ for the LOWZ sample, and $f(z_{\rm CMASS})σ_8(z_{\rm CMASS})=0.426\pm 0.029$, $D_A(z_{\rm CMASS})/r_s(z_d)=9.39 \pm 0.10$, $H(z_{\rm CMASS})r_s(z_d)=(14.02\pm 0.22)10^3\,{\rm kms}^{-1}$ for the CMASS sample. We find general agreement with previous BOSS DR11 and DR12 measurements. Combining our dataset with {\it Planck15} we perform a null test of General Relativity (GR) through the $γ$-parametrisation finding $γ=0.733^{+0.068}_{-0.069}$, which is $\sim2.7σ$ away from the GR predictions.