Non-linear Evolution of Baryon Acoustic Oscillations from Improved Perturbation Theory in Real and Redshift Spaces

We study the non-linear evolution of baryon acoustic oscillations in the matter power spectrum and correlation function from the improved perturbation theory (PT). Based on the framework of renormalized PT, we apply the {\it closure approximation} that truncates the infinite series of loop contributions at one-loop order, and obtain a closed set of integral equations for power spectrum and non-linear propagator. The resultant integral expressions keep important non-perturbative properties which can dramatically improve the prediction of non-linear power spectrum. Employing the Born approximation, we then derive the analytic expressions for non-linear power spectrum and the predictions are made for non-linear evolution of baryon acoustic oscillations in power spectrum and correlation function. A detailed comparison between improved PT results and N-body simulations shows that a percent-level agreement is achieved in a certain range in power spectrum and in a rather wider range in correlation function. Combining a model of non-linear redshift-space distortion, we also evaluate the power spectrum and correlation function in correlation function. In contrast to the results in real space, the agreement between N-body simulations and improved PT predictions tends to be worse, and a more elaborate modeling for redshift-space distortion needs to be developed. Nevertheless, with currently existing model, we find that the prediction of correlation function has a sufficient accuracy compared with the cosmic-variance errors for future galaxy surveys with volume of a few (Gpc/h)^3 at z>=0.5.Comment: 25 pages, 15 figures, accepted for publication in Phys.Rev.

Baryon Acoustic Oscillations in 2D: Modeling Redshift-space Power Spectrum from Perturbation Theory

We present an improved prescription for matter power spectrum in redshift space taking a proper account of both the non-linear gravitational clustering and redshift distortion, which are of particular importance for accurately modeling baryon acoustic oscillations (BAOs). Contrary to the models of redshift distortion phenomenologically introduced but frequently used in the literature, the new model includes the corrections arising from the non-linear coupling between the density and velocity fields associated with two competitive effects of redshift distortion, i.e., Kaiser and Finger-of-God effects. Based on the improved treatment of perturbation theory for gravitational clustering, we compare our model predictions with monopole and quadrupole power spectra of N-body simulations, and an excellent agreement is achieved over the scales of BAOs. Potential impacts on constraining dark energy and modified gravity from the redshift-space power spectrum are also investigated based on the Fisher-matrix formalism. We find that the existing phenomenological models of redshift distortion produce a systematic error on measurements of the angular diameter distance and Hubble parameter by 1~2%, and the growth rate parameter by ~5%, which would become non-negligible for future galaxy surveys. Correctly modeling redshift distortion is thus essential, and the new prescription of redshift-space power spectrum including the non-linear corrections can be used as an accurate theoretical template for anisotropic BAOs.Comment: 18 pages, 10 figure

Forecasting the Cosmological Constraints with Anisotropic Baryon Acoustic Oscillations from Multipole Expansion

Baryon acoustic oscillations (BAOs) imprinted in the galaxy power spectrum can be used as a standard ruler to determine angular diameter distance and Hubble parameter at high redshift galaxies. Combining redshift distortion effect which apparently distorts the galaxy clustering pattern, we can also constrain the growth rate of large-scale structure formation. Usually, future forecast for constraining these parameters from galaxy redshift surveys has been made with a full 2D power spectrum characterized as function of wavenumber $k$ and directional cosine $\mu$ between line-of-sight direction and wave vector, i.e., $P(k,\mu)$. Here, we apply the multipole expansion to the full 2D power spectrum, and discuss how much cosmological information can be extracted from the lower-multipole spectra, taking a proper account of the non-linear effects on gravitational clustering and redshift distortion. The Fisher matrix analysis reveals that compared to the analysis with full 2D spectrum, a partial information from the monopole and quadrupole spectra generally degrades the constraints by a factor of $\sim1.3$ for each parameter. The additional information from the hexadecapole spectrum helps to improve the constraints, which lead to an almost comparable result expected from the full 2D spectrum.Comment: 12 pages, 6 figure

Scale Dependence of Halo Bispectrum from Non-Gaussian Initial Conditions in Cosmological N-body Simulations

We study the halo bispectrum from non-Gaussian initial conditions. Based on a set of large $N$-body simulations starting from initial density fields with local type non-Gaussianity, we find that the halo bispectrum exhibits a strong dependence on the shape and scale of Fourier space triangles near squeezed configurations at large scales. The amplitude of the halo bispectrum roughly scales as $f_nl^2$. The resultant scaling on the triangular shape is consistent with that predicted by Jeong & Komatsu based on perturbation theory. We systematically investigate this dependence with varying redshifts and halo mass thresholds. It is shown that the $f_nl$ dependence of the halo bispectrum is stronger for more massive haloes at higher redshifts. This feature can be a useful discriminator of inflation scenarios in future deep and wide galaxy redshift surveys.Comment: 27 pages, 10 figures; revised argument in section 6, added appendix C, JCAP accepted versio

Baryon Acoustic Oscillations in 2D II: Redshift-space halo clustering in N-body simulations

We measure the halo power spectrum in redshift space from cosmological N-body simulations, and test the analytical models of redshift distortions particularly focusing on the scales of baryon acoustic oscillations (BAOs). Remarkably, the measured halo power spectrum in redshift space exhibits a large-scale enhancement in amplitude relative to the real-space clustering, and the effect becomes significant for the massive or highly biased halo samples. These findings cannot be simply explained by the so-called streaming model frequently used in the literature. By contrast, a physically-motivated perturbation theory model developed in the previous paper reproduces the halo power spectrum very well, and the model combining a simple linear scale-dependent bias can accurately characterize the clustering anisotropies of halos in two dimensions, i.e., line-of-sight and its perpendicular directions. The results highlight the significance of non-linear coupling between density and velocity fields associated with two competing effects of redshift distortions, i.e., Kaiser and Finger-of-God effects, and a proper account of this effect would be important in accurately characterizing the BAOs in two dimensions.Comment: 15 pages, 6 figure

Gravity and Large-Scale Non-local Bias

The relationship between galaxy and matter overdensities, bias, is most often assumed to be local. This is however unstable under time evolution, we provide proofs under several sets of assumptions. In the simplest model galaxies are created locally and linearly biased at a single time, and subsequently move with the matter (no velocity bias) conserving their comoving number density (no merging). We show that, after this formation time, the bias becomes unavoidably non-local and non-linear at large scales. We identify the non-local gravitationally induced fields in which the galaxy overdensity can be expanded, showing that they can be constructed out of the invariants of the deformation tensor (Galileons). In addition, we show that this result persists if we include an arbitrary evolution of the comoving number density of tracers. We then include velocity bias, and show that new contributions appear, a dipole field being the signature at second order. We test these predictions by studying the dependence of halo overdensities in cells of fixed matter density: measurements in simulations show that departures from the mean bias relation are strongly correlated with the non-local gravitationally induced fields identified by our formalism. The effects on non-local bias seen in the simulations are most important for the most biased halos, as expected from our predictions. The non-locality seen in the simulations is not fully captured by assuming local bias in Lagrangian space. Accounting for these effects when modeling galaxy bias is essential for correctly describing the dependence on triangle shape of the galaxy bispectrum, and hence constraining cosmological parameters and primordial non-Gaussianity. We show that using our formalism we remove an important systematic in the determination of bias parameters from the galaxy bispectrum, particularly for luminous galaxies. (abridged)Comment: 26 pages, 9 figures. v2: improved appendix

Scale Dependence of the Halo Bias in General Local-Type Non-Gaussian Models I: Analytical Predictions and Consistency Relations

We investigate the clustering of halos in cosmological models starting with general local-type non-Gaussian primordial fluctuations. We employ multiple Gaussian fields and add local-type non-Gaussian corrections at arbitrary order to cover a class of models described by frequently-discussed f_nl, g_nl and \tau_nl parameterization. We derive a general formula for the halo power spectrum based on the peak-background split formalism. The resultant spectrum is characterized by only two parameters responsible for the scale-dependent bias at large scale arising from the primordial non-Gaussianities in addition to the Gaussian bias factor. We introduce a new inequality for testing non-Gaussianities originating from multi fields, which is directly accessible from the observed power spectrum. We show that this inequality is a generalization of the Suyama-Yamaguchi inequality between f_nl and \tau_nl to the primordial non-Gaussianities at arbitrary order. We also show that the amplitude of the scale-dependent bias is useful to distinguish the simplest quadratic non-Gaussianities (i.e., f_nl-type) from higher-order ones (g_nl and higher), if one measures it from multiple species of galaxies or clusters of galaxies. We discuss the validity and limitations of our analytic results by comparison with numerical simulations in an accompanying paper.Comment: 25 pages, 3 figures, typo corrected, Appendix C updated, submitted to JCA

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

Signatures of Primordial non-Gaussianities in the Matter Power-Spectrum and Bispectrum: the Time-RG Approach

We apply the time-renormalization group approach to study the effect of primordial non-Gaussianities in the non-linear evolution of cosmological dark matter density perturbations. This method improves the standard perturbation approach by solving renormalization group-like equations governing the dynamics of gravitational instability. The primordial bispectra constructed from the dark matter density contrast and the velocity fields represent initial conditions for the renormalization group flow. We consider local, equilateral and folded shapes for the initial non-Gaussianity and analyze as well the case in which the non-linear parameter f_{NL} parametrizing the strength of the non-Gaussianity depends on the momenta in Fourier space through a power-law relation, the so-called running non-Gaussianity. For the local model of non-Gaussianity we compare our findings for the power-spectrum with those of recent N-body simulations and find that they accurately fit the N-body data up to wave-numbers k \sim 0.25 h/Mpc at z=0. We also present predictions for the (reduced) matter bispectra for the various shapes of non-Gaussianity.Comment: 27 pages, 12 figures. Results and discussion for a particular case added. One figure and one reference added. Matches with the version accepted for publication in the JCAP

Redshift-space correlation functions in large galaxy cluster surveys

Large ongoing and upcoming galaxy cluster surveys in the optical, X-ray and millimetric wavelengths will provide rich samples of galaxy clusters at unprecedented depths. One key observable for constraining cosmological models is the correlation function of these objects, measured through their spectroscopic redshift. We study the redshift-space correlation functions of clusters of galaxies, averaged over finite redshift intervals, and their covariance matrices. Expanding as usual the angular anisotropy of the redshift-space correlation on Legendre polynomials, we consider the redshift-space distortions of the monopole as well as the next two multipoles, $2\ell=2$ and 4. Taking into account the Kaiser effect, we developed an analytical formalism to obtain explicit expressions of all contributions to these mean correlations and covariance matrices. We include shot-noise and sample-variance effects as well as Gaussian and non-Gaussian contributions. We obtain a reasonable agreement with numerical simulations for the mean correlations and covariance matrices on large scales ($r> 10 h^{-1}$Mpc). Redshift-space distortions amplify the monopole correlation by about $10-20$, depending on the halo mass, but the signal-to-noise ratio remains of the same order as for the real-space correlation. This distortion will be significant for surveys such as DES, Erosita, and Euclid, which should also measure the quadrupole $2\ell=2$. The third multipole, $2\ell=4$, may only be marginally detected by Euclid.Comment: 20 page