Constraints on primordial non-Gaussianity from WMAP7 and luminous red galaxies power spectrum and forecast for future surveys

Abstract

We place new constraints on the primordial local non-Gaussianity parameter ${f}_{\mathrm{NL}}$ using recent cosmic microwave background anisotropy and galaxy clustering data. We model the galaxy power spectrum according to the halo model, accounting for a scale-dependent bias correction proportional to ${f}_{\mathrm{NL}}/{k}^{2}$. We first constrain ${f}_{\mathrm{NL}}$ in a full 13 parameters analysis that includes 5 parameters of the halo model and 7 cosmological parameters. Using the WMAP7 CMB data and the SDSS DR4 galaxy power spectrum, we find ${f}_{\mathrm{NL}}={171}_{\ensuremath{-}139}^{+140}$ at 68% C.L. and $\ensuremath{-}69<{f}_{\mathrm{NL}}<+492$ at 95% C.L. We discuss the degeneracies between ${f}_{\mathrm{NL}}$ and other cosmological parameters. Including SN-Ia data and priors on ${H}_{0}$ from Hubble Space Telescope observations we find a stronger bound: $\ensuremath{-}35<{f}_{\mathrm{NL}}<+479$ at 95%. We also fit the more recent SDSS DR7 halo power spectrum data finding, for a $\ensuremath{\Lambda}\mathrm{CDM}+{f}_{\mathrm{NL}}$ model, ${f}_{\mathrm{NL}}=\ensuremath{-}93\ifmmode\pm\else\textpm\fi{}128$ at 68% C.L. and $\ensuremath{-}327<{f}_{\mathrm{NL}}<+177$ at 95% C.L. We finally forecast the constraints on ${f}_{\mathrm{NL}}$ from future surveys as EUCLID and from CMB missions as Planck showing that their combined analysis could detect ${f}_{\mathrm{NL}}\ensuremath{\sim}5$.