FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory

McEwen, Joseph E.; Fang, X.; Hirata, Christopher M.; Blazek, Jonathan

doi:10.1088/1475-7516/2016/09/015

Cited by 157 publications

(211 citation statements)

References 67 publications

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“…A shortcoming of SPT is that the sum of P 22 (k) and P 13 (k) terms tends to cancel out at large wavenumbers, leading to unstable numerical predictions. Regularizations of these terms [31] are known to stabilize the calculation in the presence of these large cancellations. In the case of unequal time correlations, the re-scaling of each term by powers of the growth factor break the exact cancellation, allowing for better numerical convergence (Eq.…”

Section: Standard Perturbation Theorymentioning

confidence: 99%

Unequal time correlators and the Zel’dovich approximation

Chisari

Pontzen

2019

Phys. Rev. D

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The modeling of cosmological observables is based on the statistics of the matter density, velocity and gravitational fields in the Universe as a function of time. Typically, calculations are restricted to "equal time" correlations, where any given fields are evaluated at the same redshift. For some applications, it is necessary to make accurate predictions of "unequal time correlators", where the fields considered are evaluated at different redshifts. In this work, we show that the Zel'dovich approximation provides an accurate (< 10%) analytical prescription to model unequal time correlators, which we validate against numerical N-body simulations. The Zel'dovich approximation introduces a scale-dependent exponential suppression of unequal time correlators, which depends on cosmology and the redshifts of the fields considered. Comparing the Zel'dovich case to previous approximations, we show that it can yield accurate predictions for wavenumbers that extend well into the nonlinear regime. However, we also show that correlations over such scales are typically suppressed by the geometry of the lightcone, and thus should normally be negligible for cosmology with galaxy surveys. We discuss potential exceptions, such as intrinsic galaxy alignments, where unequal time correlators could play a role in the modeling of the observables. * elisa.chisari@physics.ox.ac.uk † a.pontzen@ucl.ac.uk 1 http://www.lsst.org 2 sci.esa.int/euclid/ 3 http://WFIRST.gsfc.nasa.gov

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Section: Standard Perturbation Theorymentioning

confidence: 99%

Unequal time correlators and the Zel’dovich approximation

Chisari

Pontzen

2019

Phys. Rev. D

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“…Recently, a novel algorithm for fast computation has been proposed [36,37]. In general structure formation scenarios including modified gravity, such a fast algorithm is no longer adequate, however, statistical isotropy still enables us to reduce these integrals to two-dimensional, which can be quickly evaluated with standard Gaussian quadrature.…”

Section: A Standard Ptmentioning

confidence: 99%

Constructing perturbation theory kernels for large-scale structure in generalized cosmologies

Taruya

2016

Phys. Rev. D

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We present a simple numerical scheme for perturbation theory (PT) calculations of large-scale structure. Solving the evolution equations for perturbations numerically, we construct the PT kernels as building blocks of statistical calculations, from which the power spectrum and/or correlation function can be systematically computed. The scheme is especially applicable to the generalized structure formation including modified gravity, in which the analytic construction of PT kernels is intractable. As an illustration, we show several examples for power spectrum calculations in f (R) gravity and ΛCDM models.

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“…Performing a full MCMC analysis for the Fourier space power spectrum was unfeasible for a long time because the calculation of perturbation theory convolution integrals was not fast enough. Recently, there have been a number of attempts to boost the computational efficiency by using some advanced numerical algorithms [45][46][47][48]. In our work we will employ the FFTLog method originally proposed in Ref.…”

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confidence: 99%

Measuring neutrino masses with large-scale structure: Euclid forecast with controlled theoretical error

Chudaykin

Ivanov

2019

J. Cosmol. Astropart. Phys.

148

171

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We present a Markov-Chain Monte-Carlo (MCMC) forecast for the precision of neutrino mass and cosmological parameter measurements with a Euclidlike galaxy clustering survey. We use a complete perturbation theory model for the galaxy one-loop power spectrum and tree-level bispectrum, which includes bias, redshift space distortions, IR resummation for baryon acoustic oscillations and UV counterterms. The latter encapsulate various effects of short-scale dynamics which cannot be modeled within perturbation theory. Our MCMC procedure consistently computes the non-linear power spectra and bispectra as we scan over different cosmologies. The second ingredient of our approach is the theoretical error covariance which captures uncertainties due to higher-order non-linear corrections omitted in our model. Having specified characteristics of a Euclid-like spectroscopic survey, we generate and fit mock galaxy power spectrum and bispectrum likelihoods. Our results suggest that even under very agnostic assumptions about non-linearities and short-scale physics a future Euclid-like survey will be able to measure the sum of neutrino masses with a standard deviation of 28 meV. When combined with the most recent Planck likelihood, this uncertainty decreases to 19 meV. Reducing the theoretical error on the bispectrum down to the two-loop level marginally tightens the bound to 17 meV. 1 chudy@ms2.inr.ac.ru 2 mi1271@nyu.edu arXiv:1907.06666v1 [astro-ph.CO] 15 Jul 2019 exploit the potential of upcoming surveys will strongly depend on the understanding on these effects, which is not yet complete.Fortunately, the bulk of information about the neutrino free-streaming is encoded in mildly non-linear scales which can be robustly and systematically described within perturbation theory. One of the most popular approaches is Eulerian standard cosmological perturbation theory (SPT) [14]. The basic formulation of SPT, however, does not correctly capture the non-linear evolution of baryon acoustic oscillations (BAO) [15] and short-scale physics beyond the single-stream pressureless perfect fluid hydrodynamics [16][17][18]. These problems have been intensely studied in the recent years.First, it has been shown that the non-linear suppression and distortion of the BAO can be captured by a resummation of contributions describing the tidal effects of large-scale bulk flows. This procedure, called infrared (IR) resummation, is essential for an accurate description of the BAO and has been formulated within various theoretical frameworks [19][20][21][22][23][24][25]. We will adopt a systematic approach of [22,24] streamlined in the context of time-sliced perturbation theory [26].Second, we will use the effective field theory of large-scale structure (EFT) to account for the back-reaction of small scale nonlinearities on larger scales [17,27,28]. This approach removes the unphysical UV sensitivity of perturbation theory loop integrals and parameterizes the ignorance about short scale-dynamics by various effective operators in the equations of motion for ...

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FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory

Cited by 157 publications

References 67 publications

Unequal time correlators and the Zel’dovich approximation

Unequal time correlators and the Zel’dovich approximation

Constructing perturbation theory kernels for large-scale structure in generalized cosmologies

Measuring neutrino masses with large-scale structure: Euclid forecast with controlled theoretical error

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