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Register a new userFast Calculation of Nonlinear Redshift-space Galaxy Power Spectrum Including Selection Bias
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We present a fast implementation of the next-to-leading order (1-loop) redshift-space galaxy power spectrum by using FFTlog-based methods. [V. Desjacques, D. Jeong, and F. Schmidt, JCAP 1812 (12), 035] have shown that the 1-loop galaxy power spectrum in redshift space can be computed with 28 independent loop integrals with 22 bias parameters. Analytical calculation of the angular part of the loop integrals leaves the radial part in the form of a spherical Bessel transformation that is ready to be integrated numerically by using the FFTLog transformation. We find that the original 28 loop integrals can be solved with a total of 85 unique FFTLog transformations, yet leading to a few orders of magnitude speed up over traditional multi-dimensional integration. The code used in this work is publicly available at https://github.com/JosephTomlinson/GeneralBiasPk
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Future high spectroscopic resolution galaxy surveys will observe galaxies with nearly full-sky footprints. Modeling the galaxy clustering for these surveys, therefore, must include the wide-angle effect with narrow redshift binning. In particular, when the redshift-bin size is comparable to the typical peculiar velocity field, the nonlinear redshift-space distortion (RSD) effect becomes important. A naive projection of the Fourier-space RSD model to spherical harmonic space leads to diverging expressions. In this paper we present a general formalism of projecting the higher-order RSD terms into spherical harmonic space. We show that the nonlinear RSD effect, including the fingers-of-God (FoG), can be entirely attributed to a modification of the radial window function. We find that while linear RSD enhances the harmonic-space power spectrum, unlike the three-dimensional case, the enhancement decreases on small angular-scales. The fingers-of-God suppress the angular power spectrum on all transverse scales if the bin size is smaller than $Delta r lesssim pi sigma_u$; for example, the radial bin sizes corresponding to a spectral resolution $R=lambda/Delta lambda$ of a few hundred satisfy the condition. We also provide the flat-sky approximation which reproduces the full calculation to sub-percent accuracy.
We study an efficient way to enhance the measurability of the galaxy density and/or velocity power spectrum in redshift space. It is based on the angular decomposition with the Tripolar spherical harmonic (TripoSH) basis and applicable even to galaxy distributions in wide-angle galaxy surveys. While nontrivial multipole-mode mixings are inevitable in the covariance of the Legendre decomposition coefficient commonly used in the small-angle power spectrum analysis, our analytic computation of the covariance of the TripoSH decomposition coefficient shows that such mixings are absent by virtue of high separability of the TripoSH basis, yielding the minimum variance. Via the simple signal-to-noise ratio assessment, we confirm that the detectability improvement by the TripoSH decomposition approach becomes more significant at higher multipole modes, and, e.g., the hexadecapole of the density power spectrum has two orders of magnitude improvement. The TripoSH decomposition approach is expected to be applied to not only currently available survey data but also forthcoming wide-angle one, and to bring about something new or much more accurate cosmological information.
Future or ongoing galaxy redshift surveys can put stringent constraints on neutrinos masses via the high-precision measurements of galaxy power spectrum, when combined with cosmic microwave background (CMB) information. In this paper we develop a method to model galaxy power spectrum in the weakly nonlinear regime for a mixed dark matter (CDM plus finite-mass neutrinos) model, based on perturbation theory (PT) whose validity is well tested by simulations for a CDM model. In doing this we carefully study various aspects of the nonlinear clustering and then arrive at a useful approximation allowing for a quick computation of the nonlinear power spectrum as in the CDM case. The nonlinear galaxy bias is also included in a self-consistent manner within the PT framework. Thus the use of our PT model can give a more robust understanding of the measured galaxy power spectrum as well as allow for higher sensitivity to neutrino masses due to the gain of Fourier modes beyond the linear regime. Based on the Fisher matrix formalism, we find that BOSS or Stage-III type survey, when combined with Planck CMB information, gives a precision of total neutrino mass constraint, sigma(m_nu,tot) 0.1eV, while Stage-IV type survey may achieve sigma(m_nu,tot) 0.05eV, i.e. more than a 1-sigma detection of neutrino masses. We also discuss possible systematic errors on dark energy parameters caused by the neutrino mass uncertainty. The significant correlation between neutrino mass and dark energy parameters is found, if the information on power spectrum amplitude is included. More importantly, for Stage-IV type survey, a best-fit dark energy model may be biased and falsely away from the underlying true model by more than the 1-sigma statistical errors, if neutrino mass is ignored in the model fitting.
We develop a framework to compute the redshift space power spectrum (PS), with kernels beyond Einstein-de Sitter (EdS), that can be applied to a wide variety of generalized cosmologies. We build upon a formalism that was recently employed for standard cosmology in Chen, Vlah & White (2020), and utilize an expansion of the density-weighted velocity moment generating function that explicitly separates the magnitude of the $k$-modes and their angle to the line-of-sight direction dependencies. We compute the PS for matter and biased tracers to 1-loop Perturbation Theory (PT) and show that the expansion has a correct infrared and ultraviolet behavior, free of unwanted divergences. We also add Effective Field Theory (EFT) counterterms, necessary to account for small-scale contributions to PT, and employ an IR-resummation prescription to properly model the smearing of the BAO due to large scale bulk flows within Standard-PT. To demonstrate the applicability of our formalism, we apply it on the $Lambda$CDM and the Hu-Sawicki $f(R)$ models, and compare our numerical results against the ELEPHANT suite of $N$-body simulations, finding very good agreement up to $k= 0.27, text{Mpc}^{-1} h$ at $z=0.5$ for the first three non-vanishing Legendre multipoles of the PS. To our knowledge, the model presented in this work is the most accurate theoretical EFT-PT for modified gravity to date, being the only one that accounts for beyond linear local biasing in redshift-space. Hence, we argue our RSD modeling is a promising tool to construct theoretical templates in order to test deviations from $Lambda$CDM using real data obtained from the next stage of cosmological surveys such as DESI and LSST.
We present a joint likelihood analysis of the real-space power spectrum and bispectrum measured from a variety of halo and galaxy mock catalogs. A novel aspect of this work is the inclusion of nonlinear triangle configurations for the bispectrum, made possible by a complete next-to-leading order (one-loop) description of galaxy bias, as is already common practice for the power spectrum. Based on the goodness-of-fit and the unbiasedness of the parameter posteriors, we accomplish a stringent validation of this model compared to the leading order (tree-level) bispectrum. Using measurement uncertainties that correspond to an effective survey volume of $6,(mathrm{Gpc}/h)^3$, we determine that the one-loop corrections roughly double the applicable range of scales, from $sim 0.17,h/mathrm{Mpc}$ (tree-level) to $sim 0.3,h/mathrm{Mpc}$. This converts into a $1.5 - 2$x improvement on constraints of the linear bias parameter at fixed cosmology, and a $1.5 - 2.4$x shrinkage of uncertainties on the amplitude of fluctuations $A_s$, which clearly demonstrates the benefit of extracting information from nonlinear scales despite having to marginalize over a larger number of bias parameters. Besides, our precise measurements of galaxy bias parameters up to fourth order allow for thorough comparisons to coevolution relations, showing excellent agreement for all contributions generated by the nonlocal action of gravity. Using these relations in the likelihood analysis does not compromise the model validity and is crucial for obtaining the quoted improvements on $A_s$. We also analyzed the impact of higher-derivative and scale-dependent stochastic terms, finding that for a subset of our tracers the former can boost the performance of the tree-level model with constraints on $A_s$ that are only slightly degraded compared to the one-loop model.
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