Final Report: Development of Axially Symmetric Achromatic Mirror Lenses sub-100nm Focus
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Yun, Wenbing↗
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All-glass metasurface laser optics for lensing, antireflections, and waveplates
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Lasers↗
CMB-S4: Iterative Internal Delensing and r Constraints
Abstract The tightest constraints on the tensor-to-scalar ratio r can only be obtained after removing a substantial fraction of the lensing B -mode sample variance. The planned Cosmic Microwave Background (CMB)-S4 experiment ( cmb-s4.org ) will remove the lensing B -mode signal internally by reconstructing the gravitational lenses from high-resolution observations. We document here a first lensing reconstruction pipeline able to achieve this optimally for arbitrary sky coverage. We make it part of a map-based framework to test CMB-S4 delensing performance and its constraining power on r , including inhomogeneous noise and two non-Gaussian Galactic polarized foreground models. The framework performs component separation of the high-resolution maps, followed by the construction of lensing B -mode templates, which are then included in a parametric small-aperture map cross-spectra-based likelihood for r . We find that the lensing reconstruction and framework achieve the expected performance, compatible with the target σ ( r ) ≃ 5 · 10 −4 in the absence of a tensor signal, after an effective removal of 92%–93% of the lensing B -mode variance, depending on the simulation set. The code for the lensing reconstruction can also be used for cross-correlation studies with large-scale structures, lensing spectrum reconstruction, cluster lensing, or other CMB lensing-related purposes. As part of our tests, we also demonstrate the joint optimal reconstruction of the lensing potential with the lensing curl potential mode at second order in the density fluctuations.
Astronomy & Astrophysics↗
Hubble Asteroid Hunter
Context: The Hubble Space Telescope (HST) archives constitute a rich dataset of high-resolution images to mine for strong gravitational lenses. While many HST programmes specifically target strong lenses, they can also be present by coincidence in other HST observations. Aims: Our aim is to identify non-targeted strong gravitational lenses, without any prior selection on the lens properties, in almost two decades of images from the ESA HST archive (eHST). Methods: We used crowdsourcing on the Hubble Asteroid Hunter (HAH) citizen science project to identify strong lenses, along with asteroid trails, in publicly available large field-of-view HST images. We visually inspected 2354 objects tagged by citizen scientists as strong lenses to clean the sample and identify the genuine lenses. Results: We report the detection of 252 strong gravitational lens candidates, which were not the primary targets of the HST observations. A total of 198 of them are new, not previously reported by other studies, consisting of 45 A grades, 74 B grades and 79 C grades. The majority are galaxy-galaxy configurations. The newly detected lenses are, on average, 1.3 magnitudes fainter than previous HST searches. This sample of strong lenses with high-resolution HST imaging is ideal to follow up with spectroscopy for lens modelling and scientific analyses. Conclusions: This paper presents the unbiased search of lenses that enabled us to find a wide variety of lens configurations, including exotic lenses. We demonstrate the power of crowdsourcing in visually identifying strong lenses and the benefits of exploring large archival datasets. This study shows the potential of using crowdsourcing in combination with artificial intelligence for the detection and validation of strong lenses in future large-scale surveys such as ESA’s Euclid mission or in James Webb Space Telescope (JWST) archival images.
79 ASTRONOMY AND ASTROPHYSICS↗
Correcting for Selection Biases in the Determination of the Hubble Constant from Time-Delay Cosmography
The time delay between multiple images of strongly lensed quasars has been used to infer the Hubble constant. The primary systematic uncertainty for time-delay cosmography is the mass-sheet transform (MST), which preserves the lensing observables while altering the inferred H 0 . The TDCOSMO collaboration used velocity dispersion measurements of lensed quasars and lensed galaxies to infer that mass sheets are present, which decrease the inferred H 0 by 8 per cent. Here, we test the assumption that the density profiles of galaxy–galaxy and galaxy–quasar lenses are the same. We use a composite star-plus-dark-matter mass profile for the parent deflector population and model the selection function for galaxy–galaxy and galaxy–quasar lenses. We find that a power-law density profile with an MST is a good approximation to a two-component mass profile around the Einstein radius, but we find that galaxy–galaxy lenses have systematically higher mass-sheet components than galaxy–quasar lenses. For individual systems, λ int correlates with the ratio of the half-light radius and Einstein radius of the lens. By propagating these results through the TDCOSMO hierarchical inference code, we find that H 0 is lowered by a further 3 per cent. Using a more recent measurement of velocity dispersions and our fiducial model for selection biases, we infer H 0 = 66 ± 4 (stat) ± 1 (model sys) ± 2 (measurement sys) km s -1 Mpc -1 for the TDCOSMO plus SLACS data set. The first residual systematic error is due to plausible alternative choices in modelling the selection function, and the second is an estimate of the remaining systematic error in the measurement of velocity dispersions for SLACS lenses. Accurate time-delay cosmography requires precise velocity dispersion measurements and accurate calibration of selection biases.
79 ASTRONOMY AND ASTROPHYSICS↗
The Atacama Cosmology Telescope: delensed power spectra and parameters
We present ΛCDM cosmological parameter constraints obtained from delensed microwave background power spectra. Lensing maps from a subset of DR4 data from the Atacama Cosmology Telescope (ACT) are used to undo the lensing effect in ACT spectra observed at 150 and 98 GHz. At 150 GHz, we remove the lensing distortion with an effective efficiency of 30% (TT), 30% (EE), 26% (TE) and 20% (BB); this results in detections of the delensing effect at 8.7σ (TT), 5.1σ (EE), 2.6σ (TE), and 2.4σ (BB) significance. The combination of 150 and 98 GHz TT, EE, and TE delensed spectra is well fit by a standard ΛCDM model. We also measure the shift in best-fit parameters when fitting delensed versus lensed spectra; while this shift does not inform our ability to measure cosmological parameters, it does provide a three-way consistency check among the lensing inferred from the best-fit parameters, the lensing in the CMB power spectrum, and the reconstructed lensing map. This shift is predicted to be zero when fitting with the correct model since both lensed and delensed spectra originate from the same region of sky. Furthermore, fitting with a ΛCDM model and marginalizing over foregrounds, we find that the shift in cosmological parameters is consistent with zero. Our results show that gravitational lensing of the microwave background is internally consistent within the framework of the standard cosmological model.
79 ASTRONOMY AND ASTROPHYSICS↗
Improved time-delay lens modelling and H 0 inference with transient sources
ABSTRACT Strongly lensed explosive transients such as supernovae, gamma-ray bursts, fast radio bursts, and gravitational waves are very promising tools to determine the Hubble constant (H0) in the near future in addition to strongly lensed quasars. In this work, we show that the transient nature of the point source provides an advantage over quasars: The lensed host galaxy can be observed before or after the transient’s appearance. Therefore, the lens model can be derived from images free of contamination from bright point sources. We quantify this advantage by comparing the precision of a lens model obtained from the same lenses with and without point sources. Based on Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) observations with the same sets of lensing parameters, we simulate realistic mock data sets of 48 quasar lensing systems (i.e. adding AGN in the galaxy centre) and 48 galaxy–galaxy lensing systems (assuming the transient source is not visible but the time delay and image positions have been or will be measured). We then model the images and compare the inferences of the lens model parameters and H0. We find that the precision of the lens models (in terms of the deflector mass slope) is better by a factor of 4.1 for the sample without lensed point sources, resulting in an increase of H0 precision by a factor of 2.9. The opportunity to observe the lens systems without the transient point sources provides an additional advantage for time-delay cosmography over lensed quasars. It facilitates the determination of higher signal-to-noise stellar kinematics of the main deflector, and thus its mass density profile, which, in turn plays a key role in breaking the mass-sheet degeneracy and constraining H0.
Ding, Xuheng↗
ML-driven Strong Lens Discoveries: Down to θ E ~ $0^{_{''}}_{^.}03$ and M halo < 10 11 M ⊙
We present results on extending the strong lens discovery space down to much smaller Einstein radii ( θ E ≲ $0^{_{''}}_{^.}03$) and much lower halo mass (M halo < 10 11 M ⊙ ) through the combination of JWST observations and machine learning (ML) techniques. First, we forecast detectable strong lenses with JWST using CosmoDC2 as the lens catalog, and a source catalog down to 29th magnitude. By further incorporating the VELA hydrodynamical simulations of high-redshift galaxies, we simulate strong lenses. We train a ResNet on these images, achieving near-100% completeness and purity for “conventional” strong lenses ( θ E ≳ $0^{_{''}}_{^.}05$), applicable to JWST, the Hubble Space Telescope (HST), the Roman Space Telescope, and Euclid VIS. For the first time, we also search for very low halo mass strong lenses (M halo < 10 11 M ⊙ ) in simulations, with θ E << $0^{_{''}}_{^.}05$, down to the best resolution ($0^{_{''}}_{^.}03$) and depth (10,000 s) limits of JWST using ResNet. A U-Net model is employed to pinpoint these small lenses in images, which are otherwise virtually impossible for human detection. Our results indicate that JWST can find ∼17/deg 2 such low-halo-mass lenses, with the locations of ∼1.1/deg 2 of these detectable by the U-Net at ∼100% precision (and ∼7.0/deg 2 at a 99.0% precision). To validate our model for finding “conventional” strong lenses, we apply it to HST images, discovering two new strong lens candidates previously missed by human classifiers in a crowdsourcing project (E. O. Garvin et al. 2022). This study demonstrates the (potentially “superhuman”) advantages of ML combined with current and future space telescopes for detecting conventional, and especially, low-halo-mass strong lenses, which are critical for testing cold dark matter models.
Silver, Ethan [Harvard University, Cambridge, MA (↗
TDCOSMO - IV. Hierarchical time-delay cosmography – joint inference of the Hubble constant and galaxy density profiles
The H0LiCOW collaboration inferred via strong gravitational lensing time delays a Hubble constant value of H0 = 73.3−1.8+1.7 km s−1 Mpc−1, describing deflector mass density profiles by either a power-law or stars (constant mass-to-light ratio) plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in H0. We quantify any potential effect of the MST with a flexible family of mass models, which directly encodes it, and they are hence maximally degenerate with H0. Our calculation is based on a new hierarchical Bayesian approach in which the MST is only constrained by stellar kinematics. The approach is validated on mock lenses, which are generated from hydrodynamic simulations. We first applied the inference to the TDCOSMO sample of seven lenses, six of which are from H0LiCOW, and measured H0 = 74.5−6.1+5.6 km s−1 Mpc−1. Secondly, in order to further constrain the deflector mass density profiles, we added imaging and spectroscopy for a set of 33 strong gravitational lenses from the Sloan Lens ACS (SLACS) sample. For nine of the 33 SLAC lenses, we used resolved kinematics to constrain the stellar anisotropy. From the joint hierarchical analysis of the TDCOSMO+SLACS sample, we measured H0 = 67.4−3.2+4.1 km s−1 Mpc−1. This measurement assumes that the TDCOSMO and SLACS galaxies are drawn from the same parent population. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses are in mutual statistical agreement. The TDCOSMO+SLACS analysis prefers marginally shallower mass profiles than H0LiCOW or TDCOSMO-only. Without relying on the form of the mass density profile used by H0LiCOW, we achieve a ∼5% measurement of H0. While our new hierarchical analysis does not statistically invalidate the mass profile assumptions by H0LiCOW – and thus the H0 measurement relying on them – it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on H0 derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data.Key words: gravitational lensing: strong / galaxies: general / galaxies: kinematics and dynamics / distance scale / cosmological parameters / cosmology: observations⋆ The full analysis is available at https://github.com/TDCOSMO/hierarchy_analysis_2020_public.
79 ASTRONOMY AND ASTROPHYSICS↗
The Atacama Cosmology Telescope: Weighing Distant Clusters with the Most Ancient Light
We use gravitational lensing of the cosmic microwave background (CMB) to measure the mass of the most distant blindly selected sample of galaxy clusters on which a lensing measurement has been performed to date. In CMB data from the the Atacama Cosmology Telescope and the Planck satellite, we detect the stacked lensing effect from 677 near-infrared-selected galaxy clusters from the Massive and Distant Clusters of WISE Survey (MaDCoWS), which have a mean redshift of $\langle z\rangle =1.08$. There are currently no representative optical weak lensing measurements of clusters that match the distance and average mass of this sample. We detect the lensing signal with a significance of $4.2\sigma $. We model the signal with a halo model framework to find the mean mass of the population from which these clusters are drawn. Assuming that the clusters follow Navarro–Frenk–White (NFW) density profiles, we infer a mean mass of $\langle {M}_{500c}\rangle =\left(1.7\pm 0.4\right)\times {10}^{14}\,{M}_{\odot }$. We consider systematic uncertainties from cluster redshift errors, centering errors, and the shape of the NFW profile. These are all smaller than 30% of our reported uncertainty. This work highlights the potential of CMB lensing to enable cosmological constraints from the abundance of distant clusters populating ever larger volumes of the observable universe, beyond the capabilities of optical weak lensing measurements.
79 ASTRONOMY AND ASTROPHYSICS↗
Etched Silicon Planar CRL Optics for the High-Energy X-ray Diffraction Beamlines 11-ID-B and 11-ID-C at the APS
We report the focusing of high-energy X-rays is most commonly achieved by commercially available compound refractive lenses (CRL), which are added together in larger structures. There is a need for high-energy X-ray beamlines to enable focusing in only one dimension down to a few micrometers to study layered materials and thin films. High-energy X-rays above 50 keV require often 100 lenses or more, therefore it is more efficient to etch the complete arrays of lenses into a monolithic substrate like a silicon wafer. Custom lens arrays were fabricated for the high-energy x-ray beamlines 11-ID-B, and 11-ID-C at the Argonne National Laboratory. The fabrication required tuning parameters of the Bosch process to optimize the etching of deep vertical sidewalls at a reasonable speed without overheating. The beamline 11-ID-B is equipped with lens arrays of 85-110 lenses for 59 keV and 190-250 lenses for 87 keV photon energy, focusing the beam vertically below 5.0 µm at the sample positions between 1600 mm to 2100 mm. 11-ID-C has received arrays of 435 lenses that focus 106 keV X-rays to a vertical height of 2.0 µm at the sample position. In both cases, the flux density gain in the focal spot is larger than a factor of 20, relative to using slits to cut the beam size. The lens setup is permanently installed and can be moved in and out of the beam during the experiment without further alignment. The lenses have enabled operando diffraction studies on interfaces in batteries and the development of pair distribution function (PDF) analysis using grazing incidence geometry.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Lensinglike tensions in the Planck legacy release
We analyze the final release of the Planck satellite data to constrain the gravitational lensing potential in a model-independent manner. The amount of lensing determined from the smoothing of the acoustic peaks in the temperature and polarization power spectra is 2σ too high when compared with the measurements using the lensing reconstruction and 2.8σ too high when compared with Λ CDM expectation based on the "unlensed" portion of the temperature and polarization power spectra. The largest change from the previous data release is the Λ CDM expectation, driven by improved constraints to the optical depth to reionization. Here, the anomaly still is inconsistent with actual gravitational lensing, given that the lensing reconstruction constraints are discrepant independent of the model. Within the context of Λ CDM, improvements in its parameter constraints from lensing reconstruction bring this tension to 2.1σ and from further adding baryon acoustic oscillation and Pantheon supernova data to a marginally higher 2.2σ. Once these other measurements are included, marginalizing this lensing-like anomaly cannot substantially resolve tensions with low-redshift measurements of H 0 and S 8 in Λ CDM, Λ CDM + N eff or ΛCDM + Σm ν ; furthermore the artificial strengthening of constraints on Σm ν is less than 20%.
79 ASTRONOMY AND ASTROPHYSICS↗
Simons Observatory: Constraining inflationary gravitational waves with multitracer B-mode delensing
We introduce and validate a delensing framework for the Simons Observatory (SO), which will be used to improve constraints on inflationary gravitational waves by reducing the lensing noise in measurements of the B modes in CMB polarization. SO will initially observe CMB by using three small aperture telescopes and one large-aperture telescope. While polarization maps from small-aperture telescopes will be used to constrain inflationary gravitational waves, the internal CMB lensing maps used to delens will be reconstructed from data from the large-aperture telescope. Since lensing maps obtained from the SO data will be noise dominated on subdegree scales, the SO lensing framework constructs a template for lensing-induced B modes by combining internal CMB lensing maps with maps of the cosmic infrared background from Planck as well as galaxy density maps from the LSST survey. We construct a likelihood for constraining the tensor-to-scalar ratio r that contains auto and cross spectra between observed B modes and the lensing B-mode template. We test our delensing analysis pipeline on map-based simulations containing survey nonidealities, but that, for this initial exploration, does not include contamination from Galactic and extragalactic foregrounds. We find that the SO survey masking and inhomogeneous and atmospheric noise have very little impact on the delensing performance, and the r constraint becomes σ(r)≈0.0015 which is close to that obtained from the idealized forecasts in the absence of the Galactic foreground and is nearly a factor of 2 tighter than without delensing. We also find that uncertainties in the external large-scale structure tracers used in our multitracer delensing pipeline lead to bias much smaller than the 1σ statistical uncertainties.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The DESI Single Fiber Lens Search. I. Four Thousand Spectroscopically Selected Galaxy–Galaxy Gravitational Lens Candidates
We present 4110 strong gravitational lens candidates, 3887 of which are new discoveries, selected from a sample of 5,837,154 luminous red galaxies (LRGs) observed with the Dark Energy Spectroscopic Instrument (DESI). Candidates are identified via the presence of background ionized oxygen [O II ] nebular emission lines in the foreground LRG spectra, which may originate from the lensing of higher-redshift star-forming galaxies. Using the measured foreground redshift, background redshift, and integrated flux of the background [O II ] doublet, we integrate over impact parameters to compute the probability that each candidate is a lens. We expect 53% of candidates to be true lenses with Einstein radii ranging from 0$^{''}_.$1–4", which can be confirmed with high-resolution imaging. Confirmed strong lenses from this sample will form a valuable cosmological data set, as strong gravitational lensing is the only method to directly measure dark matter halo substructure at cosmological distances. We independently recover the host of the multiply imaged gravitationally lensed type Ia supernova iPTF16geu. Monitoring these lenses for future multiply lensed transients will enable (a) H 0 measurements via time-delay cosmography and (b) substructure measurements via flux ratios.
Karp, Juliana S. M. [Univ. of Washington, Seattle,↗
SDSS-IV MaNGA: a catalogue of spectroscopically detected strong galaxy–galaxy lens candidates
ABSTRACT We spectroscopically detected candidate emission-lines of 8 likely, 17 probable, and 69 possible strong galaxy–galaxy gravitational lens candidates found within the spectra of $\approx 10\, 000$ galaxy targets contained within the completed Mapping of Nearby Galaxies at Apache Point Observatory survey. This search is based upon the methodology of the Spectroscopic Identification of Lensing Objects project, which extends the spectroscopic detection methods of the BOSS Emission-Line Lensing Survey and the Sloan Lens ACS Survey. We scanned the co-added residuals that we constructed from stacks of foreground subtracted row-stacked-spectra so a sigma-clipping method can be used to reject cosmic rays and other forms of transients that impact only a small fraction of the combined exposures. We also constructed narrow-band images from the signal to noise of the co-added residuals to observe signs of lensed source images. We also use several methods to compute the probable strong lensing regime for each candidate lens to determine which candidate background galaxies may reside sufficiently near the galaxy centre for strong lensing to occur. We present the spectroscopic redshifts within a value-added catalogue (VAC) for data release 17 (DR17) of SDSS-IV. We also present the lens candidates, spectroscopic data, and narrow-band images within a VAC for DR17. High resolution follow-up imaging of these lens candidates are expected to yield a sample of confirmed grade-A lenses with sufficient angular size to probe possible discrepancies between the mass derived from a best-fitting lens model, and the dynamical mass derived from the observed stellar velocities.
79 ASTRONOMY AND ASTROPHYSICS↗
Polymer Stabilized Paraboloid Liquid Crystal Microlenses with Integrated Pancharatnam–Berry Phase
Aspheric lenses reduce aberration and provide sharper images with improved spot size compared to spherical lenses. Here this paper demonstrates that applying shear flow can produce plano-concave liquid crystal (LC) lens arrays with paraboloid aspheric profiles. The focal length of individual lenses, with a 0.2 mm aperture, decreases from 0.67 to 0.45 mm as the chiral dopant increases from 0 to 6 wt%. The focal length is also sensitive to the polarization state of the incoming light. The lenses are stabilized by photopolymerizing with 6 wt% of reactive monomer added to the LC. A qualitative explanation for the flow-induced lens formation and the optical properties of the lenses is provided. The potential tunability of the lenses in various fields and their use as paraboloid reflectors are discussed.
36 MATERIALS SCIENCE↗
Planck 2018 results. VI. Cosmological parameters
In this paper, we present cosmological parameter results from the final full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters. Improved modelling of the small-scale polarization leads to more robust constraints on many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5 σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ω c h 2 = 0.120 ± 0.001, baryon density Ω b h 2 = 0.0224 ± 0.0001, scalar spectral index n s = 0.965 ± 0.004, and optical depth τ = 0.054 ± 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100 θ * = 1.0411 ± 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H 0 = (67.4 ± 0.5) km s –1 Mpc –1 ; matter density parameter Ω m = 0.315 ± 0.007; and matter fluctuation amplitude σ 8 = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be N eff = 2.99 ± 0.17, in agreement with the Standard Model prediction N eff = 3.046, and find that the neutrino mass is tightly constrained to Σ m ν < 0.12 eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2 σ , which pulls some parameters that affect the lensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, Ω K = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w 0 = –1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r 0.002 < 0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6 σ , tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data.
79 ASTRONOMY AND ASTROPHYSICS↗
Precise and accurate cosmology with CMB×LSS power spectra and bispectra
With the advent of a new generation of cosmological experiments that will provide high-precision measurements of the cosmic microwave background (CMB) and galaxies in the large-scale structure, it is pertinent to examine the potential of performing a joint analysis of multiple cosmological probes. In this paper, we study the cosmological information content contained in the one-loop power spectra and tree bispectra of galaxies cross-correlated with CMB lensing. We use the FFTLog method to compute angular correlations in spherical harmonic space, applicable for wide angles that can be accessed by forthcoming galaxy surveys. Here, we find that adding the bispectra and cross-correlations with CMB lensing offers a significant improvement in parameter constraints, including those on the total neutrino mass, M ν , and local non-Gaussianity amplitude, ƒ NL . In particular, our results suggest that the combination of the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) and CMB-S4 will be able to achieve σ(M ν )=42 meV from galaxy and CMB lensing correlations, and σ(M ν )=12 meV when further combined with the CMB temperature and polarization data, without any prior on the optical depth.
79 ASTRONOMY AND ASTROPHYSICS↗