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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Cosmic shear in harmonic space from the Dark Energy Survey Year 1 Data: compatibility with configuration space results

ABSTRACT We perform a cosmic shear analysis in harmonic space using the first year of data collected by the Dark Energy Survey (DES-Y1). We measure the cosmic weak lensing shear power spectra using the metacalibration catalogue and perform a likelihood analysis within the framework of CosmoSIS. We set scale cuts based on baryonic effects contamination and model redshift and shear calibration uncertainties as well as intrinsic alignments. We adopt as fiducial covariance matrix an analytical computation accounting for the mask geometry in the Gaussian term, including non-Gaussian contributions. A suite of 1200 lognormal simulations is used to validate the harmonic space pipeline and the covariance matrix. We perform a series of stress tests to gauge the robustness of the harmonic space analysis. Finally, we use the DES-Y1 pipeline in configuration space to perform a similar likelihood analysis and compare both results, demonstrating their compatibility in estimating the cosmological parameters S8, σ8, and Ωm. We use the DES-Y1 metacalibration shape catalogue, with photometric redshifts estimates in the range of 0.2−1.3, divided in four tomographic bins finding σ8(Ωm/0.3)0.5 = 0.766 ± 0.033 at 68 per cent CL. The methods implemented and validated in this paper will allow us to perform a consistent harmonic space analysis in the upcoming DES data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Studying Type II supernovae as cosmological standard candles using the Dark Energy Survey

ABSTRACT Despite vast improvements in the measurement of the cosmological parameters, the nature of dark energy and an accurate value of the Hubble constant (H0) in the Hubble–Lemaître law remain unknown. To break the current impasse, it is necessary to develop as many independent techniques as possible, such as the use of Type II supernovae (SNe II). The goal of this paper is to demonstrate the utility of SNe II for deriving accurate extragalactic distances, which will be an asset for the next generation of telescopes where more-distant SNe II will be discovered. More specifically, we present a sample from the Dark Energy Survey Supernova Program (DES-SN) consisting of 15 SNe II with photometric and spectroscopic information spanning a redshift range up to 0.35. Combining our DES SNe with publicly available samples, and using the standard candle method (SCM), we construct the largest available Hubble diagram with SNe II in the Hubble flow (70 SNe II) and find an observed dispersion of 0.27 mag. We demonstrate that adding a colour term to the SN II standardization does not reduce the scatter in the Hubble diagram. Although SNe II are viable as distance indicators, this work points out important issues for improving their utility as independent extragalactic beacons: find new correlations, define a more standard subclass of SNe II, construct new SN II templates, and dedicate more observing time to high-redshift SNe II. Finally, for the first time, we perform simulations to estimate the redshift-dependent distance-modulus bias due to selection effects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Characterization of DESI fiber assignment incompleteness effect on 2-point clustering and mitigation methods for DR1 analysis

We present an in-depth analysis of the fiber assignment incompleteness in the Dark EnergySpectroscopic Instrument (DESI) Data Release 1 (DR1). This incompleteness is caused by therestricted mobility of the robotic fiber positioner in the DESI focal plane, which limits thenumber of galaxies that can be observed at the same time, especially at small angular separations.As a result, the observed clustering amplitude is suppressed in a scale-dependent manner, which,if not addressed, can severely impact the inference of cosmological parameters. We discuss themethods adopted for simulating fiber assignment on mocks and data. In particular, we introducethe fast fiber assignment (FFA) emulator, which was employed to obtain the power spectrumcovariance adopted for the DR1 full-shape analysis. We present the mitigation techniques,organised in two classes: measurement stage and model stage. We then use high fidelity mocks as areference to quantify both the accuracy of the FFA emulator and the effectiveness of the differentmeasurement-stage mitigation techniques. This complements the studies conducted in a parallelpaper for the model-stage techniques, namely the θ-cut approach. We find that pairwiseinverse probability (PIP) weights with angular upweighting recover the “true” clustering in allthe cases considered, in both Fourier and configuration space. Notably, we present the first everpower spectrum measurement with PIP weights from real data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Strong dependence of Type Ia supernova standardization on the local specific star formation rate

As part of an on-going effort to identify, understand and correct for astrophysics biases in the standardization of Type Ia supernovae (SN Ia) for cosmology, we have statistically classified a large sample of nearby SNe Ia into those that are located in predominantly younger or older environments. This classification is based on the specific star formation rate measured within a projected distance of 1 kpc from each SN location (LsSFR). This is an important refinement compared to using the local star formation rate directly, as it provides a normalization for relative numbers of available SN progenitors and is more robust against extinction by dust. We find that the SNe Ia in predominantly younger environments are Δ Y = 0.163 ± 0.029 mag (5.7 σ ) fainter than those in predominantly older environments after conventional light-curve standardization. This is the strongest standardized SN Ia brightness systematic connected to the host-galaxy environment measured to date. The well-established step in standardized brightnesses between SNe Ia in hosts with lower or higher total stellar masses is smaller, at Δ M = 0.119 ± 0.032 mag (4.5 σ ), for the same set of SNe Ia. When fit simultaneously, the environment-age offset remains very significant, with Δ Y = 0.129 ± 0.032 mag (4.0 σ ), while the global stellar mass step is reduced to Δ M = 0.064 ± 0.029 mag (2.2 σ ). Thus, approximately 70% of the variance from the stellar mass step is due to an underlying dependence on environment-based progenitor age. Also, we verify that using the local star formation rate alone is not as powerful as LsSFR at sorting SNe Ia into brighter and fainter subsets. Standardization that only uses the SNe Ia in younger environments reduces the total dispersion from 0.142 ± 0.008 mag to 0.120 ± 0.010 mag. Overall, we show that as environment-ages evolve with redshift, a strong bias, especially on the measurement of the derivative of the dark energy equation of state, can develop. Fortunately, data that measure and correct for this effect using our local specific star formation rate indicator, are likely to be available for many next-generation SN Ia cosmology experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Planck constraints on the tensor-to-scalar ratio

In this work, we present constraints on the tensor-to-scalar ratio r using Planck data. We use the latest release of Planck maps (PR4), processed with the NPIPE code, which produces calibrated frequency maps in temperature and polarization for all Planck channels from 30 GHz to 857 GHz using the same pipeline. We computed constraints on r using the BB angular power spectrum, and we also discuss constraints coming from the TT spectrum. Given Planck's noise level, the TT spectrum gives constraints on r that are cosmic-variance limited (with $\sigma$ r = 0.093), but we show that the marginalized posterior peaks towards negative values of r at about the 1.2$\sigma$ level. We derived Planck constraints using the BB power spectrum at both large angular scales (the 'reionization bump') and intermediate angular scales (the 'recombination bump') from $\ell$=2 to 150, and find a stronger constraint than that from TT, with $\sigma$ r = 0.069. The Planck BB spectrum shows no systematic bias, and is compatible with zero, given both the statistical noise and the systematic uncertainties. The likelihood analysis using B modes yields the constraint r < 0.158 at 95% confidence using more than 50% of the sky. This upper limit tightens to r < 0.069 when Planck EE, BB, and EB power spectra are combined consistently, and it tightens further to r < 0.056 when the Planck TT power spectrum is included in the combination. Finally, combining Planck with BICEP2/Keck 2015 data yields an upper limit of r < 0.044.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Tensor-to-scalar ratio forecasts for extended LiteBIRD frequency configurations

LiteBIRD is a planned JAXA-led cosmic microwave background (CMB) B-mode satellite experiment aiming for launch in the late 2020s, with a primary goal of detecting the imprint of primordial inflationary gravitational waves. Its current baseline focal-plane configuration includes 15 frequency bands between 40 and 402 GHz, fulfilling the mission requirements to detect the amplitude of gravitational waves with the total uncertainty on the tensor-to-scalar ratio, δr, down to δr < 0.001. A key aspect of this performance is accurate astrophysical component separation, and the ability to remove polarized thermal dust emission is particularly important. In this paper we note that the CMB frequency spectrum falls off nearly exponentially above 300 GHz relative to the thermal dust spectral energy distribution, and a relatively minor high frequency extension can therefore result in even lower uncertainties and better model reconstructions. Specifically, we compared the baseline design with five extended configurations, while varying the underlying dust modeling, in each of which the High-Frequency Telescope (HFT) frequency range was shifted logarithmically toward higher frequencies, with an upper cutoff ranging between 400 and 600 GHz. In each case, we measured the tensor-to-scalar ratio r uncertainty and bias using both parametric and minimum-variance component-separation algorithms. When the thermal dust sky model includes a spatially varying spectral index and temperature, we find that the statistical uncertainty on r after foreground cleaning may be reduced by as much as 30–50% by extending the upper limit of the frequency range from 400 to 600 GHz, with most of the improvement already gained at 500 GHz. We also note that a broader frequency range leads to higher residuals when fitting an incorrect dust model, but also it is easier to discriminate between models through higher χ 2 sensitivity. Even in the case in which the fitting procedure does not correspond to the underlying dust model in the sky, and when the highest frequency data cannot be modeled with sufficient fidelity and must be excluded from the analysis, the uncertainty on r increases by only about 5% for a 500 GHz configuration compared to the baseline.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Candidate strongly lensed type Ia supernovae in the Zwicky Transient Facility archive

Gravitationally lensed type Ia supernovae (glSNe Ia) are unique astronomical tools that can be used to study cosmological parameters, distributions of dark matter, the astrophysics of the supernovae, and the intervening lensing galaxies themselves. A small number of highly magnified glSNe Ia have been discovered by ground-based telescopes such as the Zwicky Transient Facility (ZTF), but simulations predict that a fainter, undetected population may also exist. We present a systematic search for glSNe Ia in the ZTF archive of alerts distributed from June 1 2019 to September 1 2022. Using the AMPEL platform, we developed a pipeline that distinguishes candidate glSNe Ia from other variable sources. Initial cuts were applied to the ZTF alert photometry (with constraints on the peak absolute magnitude and the distance to a catalogue-matched galaxy, as examples) before forced photometry was obtained for the remaining candidates. Additional cuts were applied to refine the candidates based on their light curve colours, lens galaxy colours, and the resulting parameters from fits to the SALT2 SN Ia template. The candidates were also cross-matched with the DESI spectroscopic catalogue. Seven transients were identified that passed all the cuts and had an associated galaxy DESI redshift, which we present as glSN Ia candidates. Although superluminous supernovae (SLSNe) cannot be fully rejected as contaminants, two events, ZTF19abpjicm and ZTF22aahmovu, are significantly different from typical SLSNe and their light curves can be modelled as two-image glSN Ia systems. From this two-image modelling, we estimate time delays of 22 ± 3 and 34 ± 1 days for the two events, respectively, which suggests that we have uncovered a population of glSNe Ia with longer time delays. The pipeline is efficient and sensitive enough to parse full alert streams. It is currently being applied to the live ZTF alert stream to identify and follow-up future candidates while active. This pipeline could be the foundation for glSNe Ia searches in future surveys, such as the Rubin Observatory Legacy Survey of Space and Time.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Biased tracers in redshift space in the EFTofLSS with exact time dependence

We study the effect of the Einstein-de Sitter (EdS) approximation on the one-loop power spectrum of galaxies in redshift space in the Effective Field Theory of Large-Scale Structure. The dark matter density perturbations and velocity divergence are treated with exact time dependence. Splitting the density perturbation into its different temporal evolutions naturally gives rise to an irreducible basis of biases. While, as in the EdS approximation, at each time this basis spans a seven-dimensional space, this space is a slightly different one, and the difference is captured by a single calculable time- and vec k-dependent function. We then compute the redshift-space galaxy one-loop power spectrum with the EdS approximation (P EdS-approx ) and without (P Exact ). For the monopole we find P 0 Exact /P 0 Ed S-approx ~ 1.003 and for the quadrupole P 2 Exact /P 2 EdS-approx ~ 1.007 at z=0.57, and sharply increasing at lower redshifts. Finally, we show that a substantial fraction of the effect remains even after allowing the bias coefficients to shift within a physically allowed range. This suggests that the EdS approximation can only fit the data to a level of precision that is roughly comparable to the precision of the next generation of cosmological surveys. Furthermore, we find that implementing the exact time dependence formalism is not demanding and is easily applicable to data. Both of these points motivate a direct study of this effect on the cosmological parameters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Flavor-specific interaction favors strong neutrino self-coupling in the early universe

Flavor-universal neutrino self-interaction has been shown to ease the tension between the values of the Hubble constant measured from early and late Universe data. Here, we introduce a self-interaction structure that is flavor-specific in the three active neutrino framework. This is motivated by the stringent constraints on new secret interactions among electron and muon neutrinos from several laboratory experiments. Our study indicates the presence of a strongly interaction mode which implies a late-decoupling of the neutrinos just prior to matter radiation equality. Using the degeneracy of the coupling strength with other cosmological parameters, we explain the origin of this new mode as a result of better fit to certain features in the CMB data. We find that if only one or two of the three active neutrino flavors are interacting, then the statistical significance of the strongly-interacting neutrino mode increases substantially relative to the flavor-universal scenario. However, the central value of the coupling strength for this interaction mode does not change by any appreciable amount in the flavor-specific cases. We also briefly analyze a scenario with more than three neutrino species of which only one is self-interacting. In none of the cases, we find a large enough Hubble constant that could resolve the so-called Hubble tension.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Constraining scale dependent growth with redshift surveys

Ongoing and future redshift surveys have the capability to measure the growth rate of large scale structure at the percent level over a broad range of redshifts, tightly constraining cosmological parameters. Beyond general relativity, however, the growth rate in the linear density perturbation regime can be not only redshift dependent but scale dependent, revealing important clues to modified gravity. We demonstrate that a fully model independent approach of binning the gravitational strength G eff (k,z) matches scalar-tensor results for the growth rate fσ 8 (k,z) to 0.02%–0.27% rms accuracy. For data of the quality of the Dark Energy Spectroscopic Instrument (DESI) we find the bin values can be constrained to 1.4%–28%. We also explore the general scalar-tensor form, constraining the amplitude and past and future scalaron mass/shape parameters. Perhaps most interesting is the strong complementarity of low redshift peculiar velocity data with DESI-like redshift space distortion measurements, enabling improvements up to a factor 6–7 on 2D joint confidence contour areas. Finally, we quantify some issues with gravity parametrizations that do not include all the key physics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Improving constraints on models addressing the Hubble tension with CMB delensing

The Hubble Tension is a well-known issue in modern cosmology that refers to the apparent disagreement in inferences of the Hubble constant H 0 as found through low-redshift observations and those derived from the ΛCDM model utilizing early universe observations. Several extensions to ΛCDM have been proposed to address the Hubble Tension that involve new ingredients or dynamics in the early universe. Reversing the effects of gravitational lensing on cosmic microwave background (CMB) maps produces sharper acoustic peaks in power spectra and allows for tighter constraints on cosmological parameters. We investigate the efficacy of CMB delensing for improving the constraints on parameters used in extensions of the ΛCDM model that are aimed at resolving the Hubble Tension (such as varying fundamental constants, contributions from early dark energy, and self-interacting dark radiation). We use Fisher forecasting to predict the expected constraints with and without this delensing procedure. We demonstrate that CMB delensing improves constraints on H 0 by ~ 20% for viable models and significantly improves constraints on parameters across the board in the low-noise regime.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

The Simons Observatory: validation of reconstructed power spectra from simulated filtered maps for the small aperture telescope survey

We present a transfer function-based method to estimate angular power spectra from filtered maps for cosmic microwave background (CMB) surveys. This is especially relevant for experiments targeting the faint primordial gravitational wave signatures in CMB polarisation at large scales, such as the Simons Observatory (SO) small aperture telescopes. While timestreams can be filtered to mitigate the contamination from low-frequency noise, usual methods that calculate the mode coupling at individual multipoles can be challenging for experiments covering large sky areas or reaching few-arcminute resolution. The method we present here, although approximate, is more practical and faster for larger data volumes. We validate it through the use of simulated observations approximating the first year of SO data, going from half-wave plate-modulated timestreams to maps, and using simulations to estimate the mixing of polarisation modes induced by an example of time-domain filtering. We show its performance through an example null test and with an end-to-end pipeline that performs inference on cosmological parameters, including the tensor-to-scalar ratio r. The performance demonstration uses simulated observations at multiple frequency bands. We find that the method can recover unbiased parameters for our simulated noise levels.

CMBR experiments↗
DOE OSTI2025

The effects of continuum fitting on Lyman-α forest correlations

Correlations of fluctuations of the flux in Lyman-α forests of high-redshift quasars have been observed by the Baryonic Acoustic Oscillation Spectroscopy Survey (BOSS) and the Dark Energy Spectroscopy Instrument (DESI) survey where they have revealed the effects of baryon acoustic oscillations (BAO). In order to fit the correlation functions to a physical model and thereby constrain cosmological parameters, it is necessary to take into account the effects of fitting the observed spectra to a template about which the fluctuations are measured. In this paper we use mock spectra to test the distortion matrix technique that has been used since the final BOSS data release to appropriately distort the models. We show that while percent-level effects on the derived forest bias parameters may be present, the technique works sufficiently well that the determination of the BAO peak position is not affected at the percent level. We introduce modifications in the technique used by DESI that were not in the original applications and suggest further possibilities for improvements.

Lyman alpha forest↗
DOE OSTI2026

Cosmological analysis of the DESI DR1 Lyα 1D power spectrum

We present the cosmological analysis of the one-dimensional Lyman-α flux power spectrum from the first data release of the Dark Energy Spectroscopic Instrument (DESI). We capture the dependence of the signal on cosmology and intergalactic medium physics using an emulator trained on a cosmological suite of hydrodynamical simulations, and we correct its predictions for the impact of astrophysical contaminants and systematics, many of these not considered in previous analyses. We employ this framework to constrain the amplitude and logarithmic slope of the linear matter power spectrum at k ★ = 0.009 km -1 s and redshift z = 3, obtaining Δ 2 ★ = 0.379 ± 0.032 and n ★ = -2.309 ± 0.019 https://github.com/igmhub/cobaya_lya_p1d. The robustness of these constraints is validated through the analysis of mocks and a large number of alternative data analysis variations, with cosmological parameters kept blinded throughout the validation process. We then combine our results with constraints from DESI BAO and temperature, polarization, and lensing measurements from Planck, ACT, and SPT-3G to set constraints on ΛCDM extensions. While our measurements do not significantly tighten the limits on the sum of neutrino masses from the combination of these probes, they sharpen the constraints on the effective number of relativistic species, N eff = 3.02 ± 0.10, the running of the spectral index, α s = 0.0014 ± 0.0041, and the running of the running, β s = -0.0006 ± 0.0048, by a factor of 1.18, 1.27, and 1.90, respectively. We conclude by outlining the improvements needed to fully reach the level of confidence implied by these uncertainties.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Going Forward with the Nancy Grace Roman Space Telescope Transient Survey: Validation of Precision Forward-modeling Photometry for Undersampled Imaging

The Nancy Grace Roman Space Telescope (Roman) is an observatory for both wide-field observations and coronagraphy that is scheduled for launch in the mid-2020s. Part of the planned survey is a deep, cadenced field or fields that enable cosmological measurements with type Ia supernovae (SNe Ia). With a pixel scale of 0$_.^"$11, the Wide Field Instrument will be undersampled, presenting a difficulty for precisely subtracting the galaxy light underneath the SNe. We use simulated data to validate the ability of a forward-model code (such codes are frequently also called “scene-modeling” codes) to perform precision supernova photometry for the Roman SN survey. Our simulation includes over 760,000 image cutouts around SNe Ia or host galaxies (~10% of a full-scale survey). To have a realistic 2D distribution of underlying galaxy light, we use the VELA simulated high-resolution images of galaxies. We run each set of cutouts through our forward-modeling code which automatically measures time-dependent SN fluxes. Given our assumed inputs of a perfect model of the instrument point-spread functions and calibration, we find biases at the millimagnitude level from this method in four red filters (Y106, J129, H158, and F184), easily meeting the 0.5% Roman inter-filter calibration requirement for a cutting-edge measurement of cosmological parameters using SNe Ia. Simulated data in the bluer Z087 filter shows larger ~ 2–3 mmg biases, also meeting this requirement, but with more room for improvement. Our forward-model code has been released on Zenodo.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Improving galaxy clustering measurements with deep learning: analysis of the DECaLS DR7 data

ABSTRACT Robust measurements of cosmological parameters from galaxy surveys rely on our understanding of systematic effects that impact the observed galaxy density field. In this paper, we present, validate, and implement the idea of adopting the systematics mitigation method of artificial neural networks for modelling the relationship between the target galaxy density field and various observational realities including but not limited to Galactic extinction, seeing, and stellar density. Our method by construction allows a wide class of models and alleviates overtraining by performing k-fold cross-validation and dimensionality reduction via backward feature elimination. By permuting the choice of the training, validation, and test sets, we construct a selection mask for the entire footprint. We apply our method on the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Emission Line Galaxies (ELGs) selection from the Dark Energy Camera Legacy Survey (DECaLS) Data Release 7 and show that the spurious large-scale contamination due to imaging systematics can be significantly reduced by up-weighting the observed galaxy density using the selection mask from the neural network and that our method is more effective than the conventional linear and quadratic polynomial functions. We perform extensive analyses on simulated mock data sets with and without systematic effects. Our analyses indicate that our methodology is more robust to overfitting compared to the conventional methods. This method can be utilized in the catalogue generation of future spectroscopic galaxy surveys such as eBOSS and Dark Energy Spectroscopic Instrument (DESI) to better mitigate observational systematics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

A framework for measuring weak-lensing magnification using the Fundamental Plane

ABSTRACT Galaxy–galaxy lensing is an essential tool for probing dark matter haloes and constraining cosmological parameters. While galaxy–galaxy lensing measurements usually rely on shear, weak-lensing magnification contains additional constraining information. Using the Fundamental Plane (FP) of elliptical galaxies to anchor the size distribution of a background population is one method that has been proposed for performing a magnification measurement. We present a formalism for using the FP residuals of elliptical galaxies to jointly estimate the foreground mass and background redshift errors for a stacked lens scenario. The FP residuals include information about weak-lensing magnification κ, and therefore foreground mass, since to first order, non-zero κ affects galaxy size but not other FP properties. We also present a modular, extensible code that implements the formalism using emulated galaxy catalogues of a photometric galaxy survey. We find that combining FP information with observed number counts of the source galaxies constrains mass and photo-z error parameters significantly better than an estimator that includes number counts only. In particular, the constraint on the mass is 17.0 per cent if FP residuals are included, as opposed to 27.7 per cent when only number counts are included. The effective size noise for a foreground lens of mass $M_\mathrm{ H}=10^{14}\, \mathrm{M}_\odot$, with a conservative selection function in size and surface brightness applied to the source population, is σκ, eff = 0.250. We discuss the improvements to our FP model necessary to make this formalism a practical companion to shear analyses in weak-lensing surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

On decoupling the integrals of cosmological perturbation theory

ABSTRACT Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher order corrections by integration over linear statistics of the density fields weighted by kernels resulting from recursive solution of the fluid equations. These integrals quickly become high dimensional and naively require increasing computational resources the higher the order of the corrections. Here, we show how to decouple the integrands that often produce this issue, enabling PT corrections to be computed as a sum of products of independent 1D integrals. Our approach is related to a commonly used method for calculating multiloop Feynman integrals in quantum field theory, the Gegenbauer Polynomial x-Space Technique. We explicitly reduce the three terms entering the 2-loop power spectrum, formally requiring 9D integrations, to sums over successive 1D radial integrals. These 1D integrals can further be performed as convolutions, rendering the scaling of this method Nglog Ng with Ng the number of grid points used for each fast Fourier transform. This method should be highly enabling for upcoming large-scale structure redshift surveys where model predictions at an enormous number of cosmological parameter combinations will be required by Monte Carlo Markov Chain searches for the best-fitting values.

Slepian, Zachary↗