Perturbation Theory for BAO reconstructed fields: one-loop results in real-space matter density field

We compute the power spectrum at one-loop order in standard perturbation theory for the matter density field to which a standard Lagrangian Baryonic acoustic oscillation (BAO) reconstruction technique is applied. The BAO reconstruction method corrects the bulk motion associated with the gravitational evolution using the inverse Zel'dovich approximation (ZA) for the smoothed density field. We find that the overall amplitude of one-loop contributions in the matter power spectrum substantially decrease after reconstruction. The reconstructed power spectrum thereby approaches the initial linear spectrum when the smoothed density field is close enough to linear, i.e., the smoothing scale $R_s$ larger than around 10$h^{-1}$Mpc. On smaller $R_s$,however, the deviation from the linear spectrum becomes significant on large scales ($k\lt R_s^{-1}$) due to the nonlinearity in the smoothed density field, and the reconstruction is inaccurate. Compared with N-body simulations, we show that the reconstructed power spectrum at one loop order agrees with simulations better than the unreconstructed power spectrum. We also calculate the tree-level bispectrum in standard perturbation theory to investigate non-Gaussianity in the reconstructed matter density field. We show that the amplitude of the bispectrum significantly decreases for small $k$ after reconstruction and that the tree-level bispectrum agrees well with N-body results in the weakly nonlinear regime.Comment: 18 pages, 7 figures, accepted for publications in PR

Primordial Non-Gaussianity and Analytical Formula for Minkowski Functionals of the Cosmic Microwave Background and Large-scale Structure

We derive analytical formulae for the Minkowski Functions of the cosmic microwave background (CMB) and large-scale structure (LSS) from primordial non-Gaussianity. These formulae enable us to estimate a non-linear coupling parameter, f_NL, directly from the CMB and LSS data without relying on numerical simulations of non-Gaussian primordial fluctuations. One can use these formulae to estimate statistical errors on f_NL from Gaussian realizations, which are much faster to generate than non-Gaussian ones, fully taking into account the cosmic/sampling variance, beam smearing, survey mask, etc. We show that the CMB data from the Wilkinson Microwave Anisotropy Probe should be sensitive to |f_NL|\simeq 40 at the 68% confidence level. The Planck data should be sensitive to |f_NL|\simeq 20. As for the LSS data, the late-time non-Gaussianity arising from gravitational instability and galaxy biasing makes it more challenging to detect primordial non-Gaussianity at low redshifts. The late-time effects obscure the primordial signals at small spatial scales. High-redshift galaxy surveys at z>2 covering \sim 10Gpc^3 volume would be required for the LSS data to detect |f_NL|\simeq 100. Minkowski Functionals are nicely complementary to the bispectrum because the Minkowski Functionals are defined in real space and the bispectrum is defined in Fourier space. This property makes the Minksowski Functionals a useful tool in the presence of real-world issues such as anisotropic noise, foreground and survey masks. Our formalism can be extended to scale-dependent f_NL easily.Comment: 16 pages, 5 figures, accepted for publication in ApJ (Vol. 653, 2006