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William Coulton

Publications and source records attributed to William Coulton.

At least 19 recordsLinked to original sources

Peering Beyond the Veil of Last Scattering: A View of the Universe with CMB Spectral Distortions

The frequency spectrum of the cosmic microwave background is the most precise blackbody ever measured in nature, with deviations constrained at the level of almost one part per million from the COBE satellite. Nevertheless, departures away from a perfect blackbody are present in standard $Λ$CDM cosmology, lurking just beneath the surface of our current observational bounds. These spectral distortions provide invaluable information on our thermal history in both the post- and pre-recombination epochs, allowing us to peer beyond last scattering and into the primordial Universe. Here, we present an overview of the underlying physics responsible for generating CMB spectral distortions at all epochs. As an illustration of this rich physics, we review a comprehensive set of mechanisms capable of generating distortions both within and beyond the standard $Λ$CDM paradigm. We also discuss the information that can be gleaned by going beyond the monopole (sky-averaged) spectrum and exploiting the spatial information present in anisotropic spectral distortions. To supplement our discussion of the diverse science of spectral distortions, we provide an overview of the upcoming and proposed experimental landscape. We highlight that the combination of the TMS, COSMO, and BISOU experiments will provide the first discovery of a monopole $y$-type distortion within the coming decade. From space, the proposed FOSSIL experiment is forecasted to improve upon the original COBE/FIRAS measurement by roughly three orders of magnitude in sensitivity, bringing with it the detection of the $Λ$CDM $μ$-type distortion sourced by the dissipation of small scale acoustic modes in the pre-recombination plasma. With transformational measurements on the horizon, CMB spectral distortions offer a uniquely sensitive probe of the thermal history of the Universe at redshifts $z \lesssim 2 \times 10^6$.

astro-ph.CO

The moving lens effect: analytical modelling and foreground suppression

The moving lens (ML) effect is a secondary anisotropy of the cosmic microwave background (CMB) generated by the transverse motion of gravitational potentials, providing a direct probe of the large-scale cosmic velocity field. Its detection relies on cross-correlating a CMB map with the transverse galaxy momentum field, constructed from the galaxy overdensity and a velocity field reconstructed from it. Restricting the reconstruction to large-scale modes strongly suppresses contamination from small-scale astrophysical foregrounds while preserving the ML signal. In this work, we develop a theoretical framework for the ML estimator and its foreground contamination. We show that the signal and foregrounds have a distinct dependence on the direction of the long-wavelength mode represented by the reconstructed galaxy velocity. In the squeezed limit enforced by the velocity reconstruction filter, the bispectrum sourcing the foreground correlation becomes independent of this direction, causing its leading contribution to vanish after angular averaging. In turn, the ML signal survives by matching this directional dependence, with its amplitude reduced only by the filtered velocity variance. Using the halo model, we derive the leading corrections beyond the squeezed limit and show that the residual contamination remains parametrically suppressed. Finally, we model the cross-correlation exactly in the curved sky, and show that it is sourced solely by the longitudinal component of the galaxy momentum field, in the form of a spin-1 $E$-mode, with all other contributions either strongly suppressed on small scales or exactly zero.

astro-ph.CO

Evidence for a thermal pressure deficit in galaxy groups from the tSZ effect and weak lensing

Measurements of the thermal Sunyaev-Zel'dovich (tSZ) effect have yet to form a consistent picture of the thermodynamic state of the gas in the intracluster medium: their interpretation is complicated by foreground contamination and uncertain halo masses. We present new measurements of the tSZ effect around the Dark Energy Spectroscopic Instrument (DESI) Luminous Red Galaxy (LRG) sample, together with galaxy-galaxy lensing (GGL) measurements that enable a like-with-like comparison to state-of-the-art hydrodynamical simulations. We robustly isolate the tSZ signal by directly modeling the dust and radio emission of the target galaxies using the Atacama Cosmology Telescope (ACT) single-channel temperature maps, substantially reducing uncertainties from astrophysical foregrounds. Across halo masses $M_{500}=10^{13}-10^{14}~M_\odot$ and redshifts $0.4<z<1$, we find that the fiducial 1 Gpc$^3$ FLAMINGO simulation significantly overpredicts the observed tSZ signal at $\lesssim3'$ (i.e., $\lesssim 4\,R_{500}$ at $z=0.7$). Even the simulation with the strongest gas expulsion---which successfully reproduces the gas density inferred from kinetic SZ measurements of the same galaxy sample---overpredicts the thermal pressure. Because the strongest feedback model already reproduces the observed gas density, the remaining discrepancy is difficult to explain with additional gas depletion alone. Instead, current hydrodynamical simulations appear to overpredict the thermal pressure of galaxy groups by a factor of two, pointing toward missing non-thermal pressure support or significant departures from hydrostatic equilibrium.

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Self-consistent secondary cosmic microwave background anisotropies and extragalactic foregrounds in the FLAMINGO simulations

Secondary anisotropies in the cosmic microwave background (CMB) contain information that can be used to test both cosmological models and models of galaxy formation. Starting from lightcone-based HEALPix maps and catalogues, we present a new set of mock CMB maps constructed in a self-consistent manner from the FLAMINGO suite of cosmological hydrodynamical simulations, including CMB lensing, thermal and kinetic Sunyaev-Zeldovich effects, cosmic infrared background, radio point source and anisotropic screening maps. We show that these simulations reproduce a wide range of observational constraints. We also compare our simulations with previous predictions based on dark matter-only simulations which generally model the secondary anisotropies independently from one another, concluding that our hydrodynamical simulation mocks perform at least as well as previous mocks in matching the observations whilst retaining self-consistency in the predictions of the different components. Using the model variations in FLAMINGO, we further explore how the signals depend on cosmology and feedback modelling, and we predict cross-correlations between some of the signals that differ significantly from those in previous mocks. The mock CMB maps should provide a valuable resource for exploring correlations between different secondary anisotropies and other large-scale structure tracers, and can be applied to forecasts for upcoming surveys.

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Field-Level Inference of Primordial Non-Gaussianity with the Quijote Simulation Suite

Local primordial non-Gaussianity, parameterised as $f_{\rm NL}^{\rm local}$, will be stringently constrained using state-of-the-art methods applied to next-generation galaxy redshift survey data. In this paper, in preparation for the upcoming data sets, we demonstrate for the first time the joint field-level inference of $f_{\rm NL}^{\rm local}$, nuisance parameters, and the initial conditions in realistic halo catalogues, ones which are generated through full dark-matter-only $N$-body simulations. The field-level inference algorithm optimally constrains $f_{\rm NL}^{\rm local}$ through a Bayesian forward-modelling approach at the field level, which outperforms traditional methods by leveraging the full statistical power of the data at the scales considered. In addition, we assess its performance under various design choices in the forward model, including tests of the structure formation model and resolution. We demonstrate the robustness of our approach by applying it to a subset of the \textit{Quijote} simulation suite, performing the inference at scales down to $k_{\rm max} \approx 0.1 h \rm{Mpc}^{-1}$. Compared with a power spectrum and bispectrum estimator, we find a $\sim1.3$ improvement in $σ(f_{\rm NL}^{\rm local})$ when applying \borg{}, while marginalising over the initial conditions and bias parameters. From the small-scale information sensitivity tests, we show that the constraints on $f_{\rm NL}^{\rm local}$ improve as we increase the resolution of the inference. These findings underscore the transformative potential of field-level inference to leverage the information available in ongoing surveys such as \textit{Euclid}, providing accurate insights into the physics of cosmic inflation and the number of fields driving it.

astro-ph.CO

Unified and consistent structure growth measurements from joint ACT, SPT and \textit{Planck} CMB lensing

We present the tightest cosmic microwave background (CMB) lensing constraints to date on the growth of structure by combining CMB lensing measurements from the Atacama Cosmology Telescope (ACT), the South Pole Telescope (SPT) and \textit{Planck}. Each of these surveys individually provides lensing measurements with similarly high statistical power, achieving signal-to-noise ratios of approximately 40. The combined lensing bandpowers represent the most precise CMB lensing power spectrum measurement to date with a signal-to-noise ratio of 61 and an amplitude of $A_\mathrm{lens}^\mathrm{recon} = 1.025 \pm 0.017$ with respect to the theory prediction from the best-fit CMB \textit{Planck}-ACT cosmology. The bandpowers from all three lensing datasets, analyzed jointly, yield a $1.6\%$ measurement of the parameter combination $S_8^\mathrm{CMBL} \equiv σ_8\,(Ω_m/0.3)^{0.25} = 0.825^{+0.015}_{-0.013}$. Including Dark Energy Spectroscopic Instrument (DESI) Baryon Acoustic Oscillation (BAO) data improves the constraint on the amplitude of matter fluctuations to $σ_8 = 0.829 \pm 0.009$ (a $1.1\%$ determination). When combining with uncalibrated supernovae from \texttt{Pantheon+}, we present a $4\%$ sound-horizon-independent estimate of $H_0=66.4\pm2.5\,\mathrm{km\,s^{-1}\,Mpc^{-1}} $. The joint lensing constraints on structure growth and present-day Hubble rate are fully consistent with a $Λ$CDM model fit to the primary CMB data from \textit{Planck} and ACT. While the precise upper limit is sensitive to the choice of data and underlying model assumptions, when varying the neutrino mass sum within the $Λ\mathrm{CDM}$ cosmological model, the combination of primary CMB, BAO and CMB lensing drives the probable upper limit for the mass sum towards lower values, comparable to the minimum mass prior required by neutrino oscillation experiments.

astro-ph.CO

A high-dynamic-range view of the growth of structure and the warm/hot Universe

Baryons heat to temperatures above $>\!\!10^5\,\mathrm{K}$ as they accrete onto massive overdensities -- galaxies, groups, clusters, and filaments -- where they ionize and become optically transparent. Deep mm-wave observations such as those with ALMA have begun to probe a handful ($\sim\,$4) of massive systems at $z\!\sim\!2-4$, while low-resolution mm-wave surveys have detected thousands of objects at arcminute resolution out to $z\!\approx\!2$. To truly advance the field of the evolution of large-scale structures, mapping the warm/hot distribution of ionized gas out to the redshift of their formation, the ESO community requires a large-aperture single-dish (sub-)mm telescope. This will need to provide several orders of magnitude higher mapping speeds than currently available while preserving the few arcsecond resolution required for imaging the gas and removing contaminating radio and dusty thermal signals across the full (sub-)mm wavelength range.

astro-ph.CO

The Atacama Cosmology Telescope: A Measurement of the DR6 CMB Lensing Power Spectrum and its Implications for Structure Growth

We present new measurements of cosmic microwave background (CMB) lensing over $9400$ sq. deg. of the sky. These lensing measurements are derived from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) CMB dataset, which consists of five seasons of ACT CMB temperature and polarization observations. We determine the amplitude of the CMB lensing power spectrum at $2.3\%$ precision ($43σ$ significance) using a novel pipeline that minimizes sensitivity to foregrounds and to noise properties. To ensure our results are robust, we analyze an extensive set of null tests, consistency tests, and systematic error estimates and employ a blinded analysis framework. The baseline spectrum is well fit by a lensing amplitude of $A_{\mathrm{lens}}=1.013\pm0.023$ relative to the Planck 2018 CMB power spectra best-fit $Λ$CDM model and $A_{\mathrm{lens}}=1.005\pm0.023$ relative to the $\text{ACT DR4} + \text{WMAP}$ best-fit model. From our lensing power spectrum measurement, we derive constraints on the parameter combination $S^{\mathrm{CMBL}}_8 \equiv σ_8 \left({Ω_m}/{0.3}\right)^{0.25}$ of $S^{\mathrm{CMBL}}_8= 0.818\pm0.022$ from ACT DR6 CMB lensing alone and $S^{\mathrm{CMBL}}_8= 0.813\pm0.018$ when combining ACT DR6 and Planck NPIPE CMB lensing power spectra. These results are in excellent agreement with $Λ$CDM model constraints from Planck or $\text{ACT DR4} + \text{WMAP}$ CMB power spectrum measurements. Our lensing measurements from redshifts $z\sim0.5$--$5$ are thus fully consistent with $Λ$CDM structure growth predictions based on CMB anisotropies probing primarily $z\sim1100$. We find no evidence for a suppression of the amplitude of cosmic structure at low redshifts

astro-ph.CO

The thermal and kinematic Sunyaev-Zeldovich effect in galaxy clusters and filaments using multifrequency temperature maps of the cosmic microwave background: Abell 399--Abell 401 cluster pair case study

We present a multifrequency and multi-instrument methodology to study the physical properties of galaxy clusters and cosmic filaments using cosmic microwave background observations. Our approach enables simultaneous measurement of both the thermal (tSZ) and kinematic Sunyaev-Zeldovich (kSZ) effects, incorporates relativistic corrections, and models astrophysical foregrounds such as thermal dust emission. We do this by jointly fitting a single physical model across multiple maps from multiple instruments at different frequencies, rather than fitting a model to a single Compton-$y$ map. We demonstrate the success of this method by fitting the Abell 399-Abell 401 galaxy cluster pair and filament system using archival data from the Planck satellite and new, targeted deep data from the Atacama Cosmology Telescope, covering 11 different frequencies over 14 maps from 30 GHz to 545 GHz. Our tSZ results are consistent with previous work using Compton-$y$ maps. We measure the line-of-sight peculiar velocities of the cluster-filament system using the kSZ effect and find statistical uncertainties on individual cluster peculiar velocities of $\lesssim $600 km s$^{-1}$, which are competitive with current state-of-the-art measurements. Additionally, we measure the optical depth of the filament component with a signal-to-noise of 8.5$σ$ and reveal hints of its morphology. This modular approach is well-suited for application to future instruments across a wide range of millimeter and sub-millimeter wavebands.

astro-ph.CO

$\texttt{GENGARS}$: Accurate non-Gaussian initial conditions with arbitrary bispectrum for N-body simulations

Primordial non-Gaussianity is predicted by various inflationary models, and N-body simulations are a crucial tool for studying its imprints on large-scale structure. In this work, we present \texttt{GENGARS} ( GEnerator of Non-Gaussian ARbitrary Shapes), a framework for generating accurate non-Gaussian initial conditions for N-body simulations. It builds upon the formulation introduced by Wagner \& Verde (2012), enabling to generate a primordial gravitational potential with a desired separable bispectrum $B_Φ(k_1,k_2,k_3)$. For the local, equilateral and orthogonal non-Gaussian templates, we benchmark our method against the well-established \texttt{2LPT-PNG} code. We show that \texttt{GENGARS} achieves improved accuracy and lower noise by suppressing spurious contributions to the primordial power spectrum. This paper aims at presenting the method, quantifying its performance and illustrating the benefits and applicable use cases over existing approaches.

astro-ph.CO

The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and $Λ$CDM Parameters

We present power spectra of the cosmic microwave background (CMB) anisotropy in temperature and polarization, measured from the Data Release 6 maps made from Atacama Cosmology Telescope (ACT) data. These cover 19,000 deg$^2$ of sky in bands centered at 98, 150 and 220 GHz, with white noise levels three times lower than Planck in polarization. We find that the ACT angular power spectra estimated over 10,000 deg$^2$, and measured to arcminute scales in TT, TE and EE, are well fit by the sum of CMB and foregrounds, where the CMB spectra are described by the $Λ$CDM model. Combining ACT with larger-scale Planck data, the joint P-ACT dataset provides tight limits on the ingredients, expansion rate, and initial conditions of the universe. We find similar constraining power, and consistent results, from either the Planck power spectra or from ACT combined with WMAP data, as well as from either temperature or polarization in the joint P-ACT dataset. When combined with CMB lensing from ACT and Planck, and baryon acoustic oscillation data from DESI DR1, we measure a baryon density of $Ω_b h^2=0.0226\pm0.0001$, a cold dark matter density of $Ω_c h^2=0.118\pm0.001$, a Hubble constant of $H_0=68.22\pm0.36$ km/s/Mpc, a spectral index of $n_s=0.974\pm0.003$, and an amplitude of density fluctuations of $σ_8=0.813\pm0.005$. Including the DESI DR2 data tightens the Hubble constant to $H_0=68.43\pm0.27$ km/s/Mpc; $Λ$CDM parameters agree between the P-ACT and DESI DR2 data at the $1.6σ$ level. We find no evidence for excess lensing in the power spectrum, and no departure from spatial flatness. The contribution from Sunyaev-Zel'dovich (SZ) anisotropy is detected at high significance; we find evidence for a tilt with suppressed small-scale power compared to our baseline SZ template spectrum, consistent with hydrodynamical simulations with feedback.

astro-ph.CO

The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models

We use new cosmic microwave background (CMB) primary temperature and polarization anisotropy measurements from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) to test foundational assumptions of the standard cosmological model and set constraints on extensions to it. We derive constraints from the ACT DR6 power spectra alone, as well as in combination with legacy data from Planck. To break geometric degeneracies, we include ACT and Planck CMB lensing data and baryon acoustic oscillation data from DESI Year-1, and further add supernovae measurements from Pantheon+ for models that affect the late-time expansion history. We verify the near-scale-invariance (running of the spectral index $d n_s/d\ln k = 0.0062 \pm 0.0052$) and adiabaticity of the primordial perturbations. Neutrino properties are consistent with Standard Model predictions: we find no evidence for new light, relativistic species that are free-streaming ($N_{\rm eff} = 2.86 \pm 0.13$, which combined with external BBN data becomes $N_{\rm eff} = 2.89 \pm 0.11$), for non-zero neutrino masses ($\sum m_ν< 0.082$ eV at 95% CL), or for neutrino self-interactions. We also find no evidence for self-interacting dark radiation ($N_{\rm idr} < 0.134$), early-universe variation of fundamental constants, early dark energy, primordial magnetic fields, or modified recombination. Our data are consistent with standard BBN, the FIRAS-inferred CMB temperature, a dark matter component that is collisionless and with only a small fraction allowed as axion-like particles, a cosmological constant, and the late-time growth rate predicted by general relativity. We find no statistically significant preference for a departure from the baseline $Λ$CDM model. In general, models introduced to increase the Hubble constant or to decrease the amplitude of density fluctuations inferred from the primary CMB are not favored by our data.

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The Spectroscopic Stage-5 Experiment

The existence, properties, and dynamics of the dark sectors of our universe pose fundamental challenges to our current model of physics, and large-scale astronomical surveys may be our only hope to unravel these long-standing mysteries. In this white paper, we describe the science motivation, instrumentation, and survey plan for the next-generation spectroscopic observatory, the Stage-5 Spectroscopic Experiment (Spec-S5). Spec-S5 is a new all-sky spectroscopic instrument optimized to efficiently carry out cosmological surveys of unprecedented scale and precision. The baseline plan for Spec-S5 involves upgrading two existing 4-m telescopes to new 6-m wide-field facilities, each with a highly multiplexed spectroscopic instrument capable of simultaneously measuring the spectra of 13,000 astronomical targets. Spec-S5, which builds and improves on the hardware used for previous cosmology experiments, represents a cost-effective and rapid approach to realizing a more than 10$\times$ gain in spectroscopic capability compared to the current state-of-the-art represented by the Dark Energy Spectroscopic Instrument project (DESI). Spec-S5 will provide a critical scientific capability in the post-Rubin and post-DESI era for advancing cosmology, fundamental physics, and astrophysics in the 2030s.

astro-ph.CO

The Atacama Cosmology Telescope: DR6 Maps

We present Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) maps of the Cosmic Microwave Background temperature and polarization anisotropy at arcminute resolution over three frequency bands centered on 98, 150 and 220 GHz. The maps are based on data collected with the AdvancedACT camera over the period 2017--2022 and cover 19,000 square degrees with a median combined depth of 10 uK arcmin. We describe the instrument, mapmaking and map properties and illustrate them with a number of figures and tables. The ACT DR6 maps and derived products are available on LAMBDA at https://lambda.gsfc.nasa.gov/product/act/actadv_prod_table.html. We also provide an interactive web atlas at https://phy-act1.princeton.edu/public/snaess/actpol/dr6/atlas and HiPS data sets in Aladin (e.g. https://alasky.cds.unistra.fr/ACT/DR4DR6/color_CMB).

astro-ph.CO

The Atacama Cosmology Telescope: DR6 Gravitational Lensing Map and Cosmological Parameters

We present cosmological constraints from a gravitational lensing mass map covering 9400 sq. deg. reconstructed from CMB measurements made by the Atacama Cosmology Telescope (ACT) from 2017 to 2021. In combination with BAO measurements (from SDSS and 6dF), we obtain the amplitude of matter fluctuations $σ_8 = 0.819 \pm 0.015$ at 1.8% precision, $S_8\equivσ_8({Ω_{\rm m}}/0.3)^{0.5}=0.840\pm0.028$ and the Hubble constant $H_0= (68.3 \pm 1.1)\, \text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$ at 1.6% precision. A joint constraint with CMB lensing measured by the Planck satellite yields even more precise values: $σ_8 = 0.812 \pm 0.013$, $S_8\equivσ_8({Ω_{\rm m}}/0.3)^{0.5}=0.831\pm0.023$ and $H_0= (68.1 \pm 1.0)\, \text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$. These measurements agree well with $Λ$CDM-model extrapolations from the CMB anisotropies measured by Planck. To compare these constraints to those from the KiDS, DES, and HSC galaxy surveys, we revisit those data sets with a uniform set of assumptions, and find $S_8$ from all three surveys are lower than that from ACT+Planck lensing by varying levels ranging from 1.7-2.1$σ$. These results motivate further measurements and comparison, not just between the CMB anisotropies and galaxy lensing, but also between CMB lensing probing $z\sim 0.5-5$ on mostly-linear scales and galaxy lensing at $z\sim 0.5$ on smaller scales. We combine our CMB lensing measurements with CMB anisotropies to constrain extensions of $Λ$CDM, limiting the sum of the neutrino masses to $\sum m_ν < 0.13$ eV (95% c.l.), for example. Our results provide independent confirmation that the universe is spatially flat, conforms with general relativity, and is described remarkably well by the $Λ$CDM model, while paving a promising path for neutrino physics with gravitational lensing from upcoming ground-based CMB surveys.

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Inflation: Theory and Observations

Cosmic inflation provides a window to the highest energy densities accessible in nature, far beyond those achievable in any realistic terrestrial experiment. Theoretical insights into the inflationary era and its observational probes may therefore shed unique light on the physical laws underlying our universe. This white paper describes our current theoretical understanding of the inflationary era, with a focus on the statistical properties of primordial fluctuations. In particular, we survey observational targets for three important signatures of inflation: primordial gravitational waves, primordial non-Gaussianity and primordial features. With the requisite advancements in analysis techniques, the tremendous increase in the raw sensitivities of upcoming and planned surveys will translate to leaps in our understanding of the inflationary paradigm and could open new frontiers for cosmology and particle physics. The combination of future theoretical and observational developments therefore offer the potential for a dramatic discovery about the nature of cosmic acceleration in the very early universe and physics on the smallest scales.

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Snowmass Theory Frontier: Astrophysics and Cosmology

We summarize progress made in theoretical astrophysics and cosmology over the past decade and areas of interest for the coming decade. This Report is prepared as the TF09 "Astrophysics and Cosmology" topical group summary for the Theory Frontier as part of the Snowmass 2021 process.

hep-ph

Biases to primordial non-Gaussianity measurements from CMB secondary anisotropies

Our view of the last-scattering surface in the cosmic microwave background (CMB) is obscured by secondary anisotropies, sourced by scattering, extragalactic emission and gravitational processes between recombination and observation. Whilst it is established that non-Gaussianity from the correlation between the integrated-Sachs-Wolfe (ISW) effect and gravitational lensing can significantly bias primordial non-Gaussianity (PNG) searches, recent work by Hill (2018) has suggested that other combinations of secondary anisotropies can also produce significant biases. Building on that work, we use the WebSky and Sehgal et al.(2010) simulations to perform an extensive examination of possible biases to PNG measurements for the local, equilateral and orthogonal shapes. For a Planck-like CMB experiment, without foreground cleaning, we find significant biases from cosmic infrared background (CIB)-lensing and thermal Sunyaev-Zel'dovich (tSZ)-lensing bispectra for the local and orthogonal templates, and from CIB and tSZ bispectra for the equilateral template. For future experiments, such as the Simons Observatory, biases from correlations between the ISW effect and the tSZ and CIB will also become important. Finally we investigate whether foreground-cleaning techniques are able to suppress these biases sufficiently. We find that the majority of these biases are effectively suppressed by the internal-linear-combination method and the total bias to Planck-like and SO-like experiments is less than the $1\,σ$ statistical error. However, the small total bias arises from the cancellation of several $1\,σ$ biases for Planck-like experiments and $2\,σ$ biases for SO-like. As this cancellation is likely sensitive to the precise modelling, to ensure robustness against these biases explicit removal methods should be used, likely at the cost of decreased constraining power.

astro-ph.CO