Next-to-leading resummation of cosmological perturbations via the Lagrangian picture: 2-loop correction in real and redshift spaces

We present an improved prediction of the nonlinear perturbation theory (PT) via the Lagrangian picture, which was originally proposed by Matsubara (2008). Based on the relations between the power spectrum in standard PT and that in Lagrangian PT, we derive analytic expressions for the power spectrum in Lagrangian PT up to 2-loop order in both real and redshift spaces. Comparing the improved prediction of Lagrangian PT with $N$-body simulations in real space, we find that the 2-loop corrections can extend the valid range of wave numbers where we can predict the power spectrum within 1% accuracy by a factor of 1.0 ($z=0.5$), 1.3 (1), 1.6 (2) and 1.8 (3) vied with 1-loop Lagrangian PT results. On the other hand, in all redshift ranges, the higher-order corrections are shown to be less significant on the two-point correlation functions around the baryon acoustic peak, because the 1-loop Lagrangian PT is already accurate enough to explain the nonlinearity on those scales in $N$-body simulations.Comment: 18pages, 4 figure

The integrated Sachs-Wolfe Effect -- Large Scale Structure Correlation

We discuss the correlation between late-time integrated Sachs-Wolfe (ISW) effect in the cosmic microwave background (CMB) temperature anisotropies and the large scale structure of the local universe. This correlation has been proposed and studied in the literature as a probe of the dark energy and its physical properties. We consider a variety of large scale structure tracers suitable for a detection of the ISW effect via a cross-correlation. In addition to luminous sources, we suggest the use of tracers such as dark matter halos or galaxy clusters. A suitable catalog of mass selected halos for this purpose can be constructed with upcoming wide-field lensing and Sunyaev-Zel'dovich (SZ) effect surveys. With multifrequency data, the presence of the ISW-large scale structure correlation can also be investigated through a cross-correlation of the frequency cleaned SZ and CMB maps. While convergence maps constructed from lensing surveys of the large scale structure via galaxy ellipticities are less correlated with the ISW effect, lensing potentials that deflect CMB photons are strongly correlated and allow, probably, the best mechanism to study the ISW-large scale structure correlation with CMB data alone.Comment: 10 Pages, PRD submitte