In this letter we present constraints on the scale-dependent "local" type primordial non-Gaussianity, which is described by non-Gaussianity's spectral index $n_{ \rm NG}$, from the NRAO VLA Sky Survey and the quasar catalog of the Sloan Digital Sky Survey (SDSS) Data Release 6, together with the SDSS Data Release 12 photo-z sample. Here, we use the auto-correlation analyses of these three probes and their cross-correlation analyses with the cosmic microwave background (CMB) temperature map, and obtain the tight constraint on the spectral index: $n_{ \rm NG}=0.2 ^{ +0.7}_{ -1.0}$ ($1\,\sigma$ C.L.), which shows the first competitive constraint on the running of non-Gaussianity from current large-scale structure clustering data. Furthermore, we also perform the forecast calculations and improve the limit of $n_{ \rm NG}$ using the future Euclid mission, and obtain the standard deviation at 68\% confidence level: $\Delta n_{ \rm NG}=1.74$ when considering the fiducial value $f_{ \rm NL}=3$, which provides the complementary constraining power to those from the CMB bispectrum information.
Categories: astro-ph.CO