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Exotic energy injection in the early Universe. II. CMB spectral distortions and constraints on light dark matter

Here, we calculate the post-recombination contribution to the cosmic microwave background (CMB) spectral distortion due to general exotic energy injections, including dark matter (DM) decaying or annihilating to Standard Model particles. Upon subtracting the background distortion that would be present even without such energy injections, we find residual distortions that are still potentially large enough to be detectable by future experiments such as PIXIE. The distortions also have a high-energy spectral feature that is a unique signature of the injection of high-energy particles. We present a calculation of the global ionization history in the presence of decaying dark matter with sub-keV masses, and also show that previous calculations of the global ionization history in the presence of energy injection are not significantly modified by these additional spectral distortions. Our improved treatment of low-energy electrons allows us to extend calculations of the CMB anisotropy constraints for decaying DM down to arbitrarily low masses. We also recast these bounds as constraints on the coupling of axionlike particles to photons.

79 ASTRONOMY AND ASTROPHYSICS↗

The Atacama Cosmology Telescope: Cosmology from Cross-correlations of unWISE Galaxies and ACT DR6 CMB Lensing

We present tomographic measurements of structure growth using cross-correlations of Atacama Cosmology Telescope (ACT) DR6 and Planck cosmic microwave background (CMB) lensing maps with the unWISE Blue and Green galaxy samples, which span the redshift ranges 0.2 ≲ z ≲ 1.1 and 0.3 ≲ z ≲ 1.8, respectively. We improve on prior unWISE cross-correlations not just by making use of the new, high-precision ACT DR6 lensing maps, but also by including additional spectroscopic data for redshift calibration and by analyzing our measurements with a more flexible theoretical model. We determine the amplitude of matter fluctuations at low redshifts (z ≃ 0.2–1.6), finding S 8 ≡ σ 8 (Ω m /0.3) 0.5 = 0.813 ± 0.021 using the ACT cross-correlation alone and S 8 = 0.810 ± 0.015 with a combination of Planck and ACT cross-correlations; these measurements are fully consistent with the predictions from primary CMB measurements assuming standard structure growth. The addition of baryon acoustic oscillation data breaks the degeneracy between σ 8 and Ω m , allowing us to measure σ 8 = 0.813 ± 0.020 from the cross-correlation of unWISE with ACT and σ 8 = 0.813 ± 0.015 from the combination of cross-correlations with ACT and Planck. These results also agree with the expectations from primary CMB extrapolations in ΛCDM cosmology; the consistency of σ 8 derived from our two redshift samples at z ∼ 0.6 and 1.1 provides a further check of our cosmological model. Our results suggest that structure formation on linear scales is well described by ΛCDM even down to low redshifts z ≲ 1.

79 ASTRONOMY AND ASTROPHYSICS↗

Four-year Cosmology Large Angular Scale Surveyor (CLASS) Observations: On-sky Receiver Performance at 40, 90, 150, and 220 GHz Frequency Bands

The Cosmology Large Angular Scale Surveyor (CLASS) observes the polarized cosmic microwave background (CMB) over the angular scales of 1° ≲ θ ≤ 90° with the aim of characterizing primordial gravitational waves and cosmic reionization. We report on the on-sky performance of the CLASS Q-band (40 GHz), W-band (90 GHz), and dichroic G-band (150/220 GHz) receivers that have been operational at the CLASS site in the Atacama desert since 2016 June, 2018 May, and 2019 September, respectively. We show that the noise-equivalent power measured by the detectors matches the expected noise model based on on-sky optical loading and lab-measured detector parameters. Using Moon, Venus, and Jupiter observations, we obtain power to antenna temperature calibrations and optical efficiencies for the telescopes. From the CMB survey data, we compute instantaneous array noise-equivalent-temperature sensitivities of 22, 19, 23, and 71 $\mu {{\rm{K}}}_{\mathrm{cmb}}\sqrt{{\rm{s}}}$ for the 40, 90, 150, and 220 GHz frequency bands, respectively. These noise temperatures refer to white noise amplitudes, which contribute to sky maps at all angular scales. Future papers will assess additional noise sources impacting larger angular scales.

Observational cosmology↗

Stacked CMB lensing and ISW signals around superstructures in the DESI Legacy Survey

The imprints of large-scale structures on the Cosmic Microwave Background (CMB) can be studied via the CMB lensing and Integrated Sachs–Wolfe (ISW) signals. In particular, the stacked ISW signal around supervoids has been claimed in several works to be anomalously high. In this study, we find cluster and void superstructures using four tomographic redshift bins with 0 < z < 0.8 from the DESI Legacy Survey and measure the stacked CMB lensing and ISW signals around them. To compare our measurements with ΛCDM model predictions, we construct a mock catalogue with matched galaxy number density and bias and apply the same photo-z uncertainty as the data. The consistency between the mock and the data is verified via the stacked galaxy density profiles around the superstructures and their quantity. The corresponding lensing convergence and ISW maps are then constructed and compared. The stacked lensing signal agrees with data well except at the highest redshift bin in density peaks, where the mock prediction is significantly higher, by approximately a factor of 1.3. The stacked ISW signal is generally consistent with the mock prediction. We do not obtain a significant signal from voids, A ISW = -0.10 ± 0.69, and the signal from clusters, A ISW = 1.52 ± 0.72, is at best weakly detected. However, these results are strongly inconsistent with previous claims of ISW signals at many times the level of the ΛCDM prediction. We discuss the comparison of our results with past work in this area and investigate possible explanations for this discrepancy.

79 ASTRONOMY AND ASTROPHYSICS↗

Enhanced matter power spectrum from axion kination after Big Bang nucleosynthesis

Despite stringent constraints from Big Bang Nucleosynthesis (BBN) and cosmic microwave background (CMB) observations, it is still possible for well-motivated particle physics models to substantially alter the cosmic expansion history between BBN and recombination. In this work we consider two different axion models that can realize a period of first matter domination, then kination, in this epoch. We perform fits to both primordial element abundances as well as CMB data and determine that up to a decade of late axion domination is allowed by these probes of the early universe. We establish the implications of late axion domination for the matter power spectrum on the scales 1/Mpc ≲ k ≲ 10 3 /Mpc. Our 'log' model predicts a relatively modest bump-like feature together with a small suppression relative to the standard ΛCDM predictions on either side of the enhancement. Our 'two-field' model predicts a larger, plateau-like feature that realizes enhancements to the matter power spectrum of up to two orders of magnitude. These features have interesting implications for structure formation at the forefront of current detection capabilities.

79 ASTRONOMY AND ASTROPHYSICS↗

Planck intermediate results. LVI. Detection of the CMB dipole through modulation of the thermal Sunyaev-Zeldovich effect: Eppur si muove II

The largest temperature anisotropy in the cosmic microwave background (CMB) is the dipole, which has been measured with increasing accuracy for more than three decades, particularly with the Planck satellite. The simplest interpretation of the dipole is that it is due to our motion with respect to the rest frame of the CMB. Since current CMB experiments infer temperature anisotropies from angular intensity variations, the dipole modulates the temperature anisotropies with the same frequency dependence as the thermal Sunyaev-Zeldovich (tSZ) effect. Here, we present the first, and significant, detection of this signal in the tSZ maps and find that it is consistent with direct measurements of the CMB dipole, as expected. The signal contributes power in the tSZ maps, which is modulated in a quadrupolar pattern, and we estimate its contribution to the tSZ bispectrum, noting that it contributes negligible noise to the bispectrum at relevant scales.

79 ASTRONOMY AND ASTROPHYSICS↗

Final Results from the BIMA CMB Anisotropy Survey and Search for Signature of the SZ Effect

We report the final results of our study of the cosmic microwave background (CMB) with the BIMA array. Over 1000 hours of observation were dedicated to this project exploring CMB anisotropy on scales between 1' and 2' in eighteen 6'.6 FWHM fields. In the analysis of the CMB power spectrum, the visibility data is divided into two bins corresponding to different angular scales. Modeling the observed excess power as a flat band of average multipole l(sub eff)= 5237, we find deltaT(sup 2)(sub 1) = 220(sup +140)(sub -120) mu K(sup 2) at 68% confidence and deltaT(sup 2)(sub 1) greater than 0 muK(sup 2) with 94.7% confidence. In a second band with average multipole of l(sub eff) = 8748, we find deltaT(sup 2)(sub 2) consistent with zero, and an upper limit 880 muK(sup 2) at 95% confidence. An extensive series of tests and supplemental observations with the VLA provide strong evidence against systematic errors or radio point sources being the source of the observed excess power. The dominant source of anisotropy on these scales is expected to arise from the Sunyaev-Zel'dovich (SZ) effect in a population of distant galaxy clusters. If the excess power is due to the SZ effect, we can place constraints on the normalization of the matter power spectrum sigma(sub 8) = 1.03(sup +0.20)(sub -0.29) at 68% confidence. The distribution of pixel fluxes in the BIMA images are found to be consistent with simulated observations of the expected SZ background and rule out instrumental noise or radio sources as the source of the observed excess power with similar confidence to the detection of excess power. Follow-up optical observations to search for galaxy over-densities anti-correlated with flux in the BIMA images, as might be expected from the SZ effect, proved to be inconclusive.

Dawson, K. S.↗

Transitioning from Stage-III to Stage-IV: Cosmology from galaxy×CMB lensing and shear×CMB lensing (Final Report for Grant SC0021429 "Cosomology with Galaxy and CMB Surveys: Mitigating Systematic Effects Through Combining Datasets")

We examine the cosmological constraining power from two cross-correlation probes between galaxy and cosmic microwave background (CMB) surveys: the cross-correlation of lens galaxy density with CMB lensing convergence $\langle δ_g$$^κ\text{CMB}\rangle$, and source galaxy weak lensing shear with CMB lensing convergence $\langle^{γκ}$$_{\text{CMB}}\rangle$. These two cross-correlation probes provide an independent cross-check of other large-scale structure constraints and are insensitive to galaxy-only or CMB-only systematic effects. In addition, when combined with other large-scale structure probes, the cross-correlations can break degeneracies in cosmological and nuisance parameters, improving both the precision and robustness of the analysis. In this work, we study how the constraining power of $\langle δ_g$$^κ\text{CMB}\rangle + \langle^{γκ}$$_{\text{CMB}}\rangle$ changes from Stage-III (ongoing) to Stage-IV (future) surveys. Given the flexibility in selecting the lens galaxy sample, we also explore systematically the impact on cosmological constraints when we vary the redshift range and magnitude limit of the lens galaxies using mock galaxy catalogs. We find that in our setup, the contribution to cosmological constraints from $\langle δ_g$$^κ\text{CMB}\rangle$ and $\langle^{γκ}$$_{\text{CMB}}\rangle$ are comparable in the Stage-III data sets; but in Stage-IV surveys, the noise in$\langle δ_g$$^κ\text{CMB}\rangle$ becomes subdominant to cosmic variance, preventing $\langle δ_g$$^κ\text{CMB}\rangle$ to further improve the constraints. This implies that to maximize the cosmological constraints from future $\langle δ_g$$^κ\text{CMB}\rangle$ + $\langle^{γκ}$$_{\text{CMB}}\rangle$ analyses, we should focus more on the requirements on$^{γκ}$$_{\text{CMB}}\rangle$ instead of$\langle δ_g$$^κ\text{CMB}\rangle$. Furthermore, the selection of the lens sample should be optimized in terms of our ability to characterize its redshift or galaxy bias instead of its number density.

79 ASTRONOMY AND ASTROPHYSICS↗

The Planck Mission

Planck, scheduled for launch in 2007, will be the third space mission to observe the cosmic microwave background (CMB). Two cryogenic instruments and an off-axis telescope will provide an unprecedented combination of sensitivity, angular resolution, and frequency coverage. Planck is designed to measure the temperature anisotropies of the CMB to limits set not by the instruments, but rather by the Universe itself. In addition, it will measure the E-type polarization of the CMB, and provide all-sky surveys at nine frequencies between 30 and 857GHz.

cosmic↗

Investigation of CMB constraints for dark matter-helium scattering

In this work, we study dark matter-helium scattering in the early Universe and its impact on constraints from cosmic microwave background (CMB) anisotropy measurements. We describe possible theoretical frameworks for dark matter-nucleon interactions via a scalar, pseudoscalar, or vector mediator; such interactions give rise to hydrogen and helium scattering, with cross sections that have a power-law dependence on relative velocity. Within these frameworks, we consider three scenarios: dark matter coupling to only neutrons, to only protons, and to neutrons and protons with equal strength. For these various cases, we use Planck 2018 temperature, polarization, and lensing anisotropy data to place constraints on dark matter scattering with hydrogen and/or helium for dark matter masses between 10 keV and 1 TeV. For any model that permits both helium and hydrogen scattering with a non-negative power-law velocity dependence, we find that helium scattering dominates the constraint for dark matter masses well above the proton mass. Furthermore, we place the first CMB constraints on dark matter that scatters dominantly/exclusively with helium in the early Universe.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Cosmic dipoles from large-scale structure surveys

Large-scale structure surveys can be used to measure the dipole in the cosmic microwave background (CMB), in the luminosity distances inferred from type-Ia supernova observations, and in the spatial distribution of galaxies and quasars. The measurements of these cosmic dipoles appear to be mutually inconsistent, even though they are expected to indicate the common observer velocity. This observational tension may represent a significant challenge to the standard model of cosmology. Here, in this work, we study in detail what contributes to the cosmic dipoles from CMB, supernova, and galaxy survey in the standard Λ cold dark matter (Λ⁢ CDM) model, though our theoretical model can be applied beyond the standard model. While measurements of the cosmic dipoles yield the relative velocities between the source samples and the observer velocity, the motion of the observer is the dominant contribution in the conformal Newtonian gauge, and the intrinsic velocities of the samples fall steeply with increasing redshift of the sources. Hence the cosmic dipoles of CMB, type-Ia supernovae, and galaxies should be aligned but can have different amplitudes. We also clarify several misconceptions that are commonly found in the literature.

cosmic microwave background↗

Cosmological Constraints From the Tomography of DES-Y3 Galaxies With CMB Lensing From ACT DR4

We present a measurement of the cross-correlation between the MAGLIM galaxies selected from the Dark Energy Survey (DES) first three years of observations (Y3) and cosmic microwave background (CMB) lensing from the Atacama Cosmology Telescope (ACT) Data Release 4 (DR4), reconstructed over ∼ 436 deg 2 of the sky. Our galaxy sample, which covers ∼ 4143 deg 2 , is divided into six redshift bins spanning the redshift range of 0.20 8 ≡ σ 8 (Ω m /0.3) 0.5 = 0.75 +0.04 -0.05 . In addition, we constrain the linear growth of cosmic structure as a function of redshift. Our results are consistent with recent DES Y3 analyses and suggest a preference for a lower S 8 compared to results from measurements of CMB anisotropies by the Planck satellite, although at a mild level (< 2σ) of statistical significance.

cosmological parameters from CMBR↗

Moment expansion of polarized dust SED: A new path towards capturing the CMB B -modes with LiteBIRD

Accurate characterization of the polarized dust emission from our Galaxy will be decisive in the quest for the cosmic microwave background (CMB) primordial B-modes. An incomplete modeling of its potentially complex spectral properties could lead to biases in the CMB polarization analyses and to a spurious measurement of the tensor-to-scalar ratio r. It is particularly crucial for future surveys like the LiteBIRD satellite, the goal of which is to constrain the faint primordial signal leftover by inflation with an accuracy on the tensor-to-scalar ratio r of the order of 10 –3 . Variations of the dust properties along and between lines of sight lead to unavoidable distortions of the spectral energy distribution (SED) that cannot be easily anticipated by standard component-separation methods. This issue can be tackled using a moment expansion of the dust SED, an innovative parametrization method imposing minimal assumptions on the sky complexity. In the present paper, we apply this formalism to the B-mode cross-angular power spectra computed from simulated LiteBIRD polarization data at frequencies between 100 and 402 GHz that contain CMB, dust, and instrumental noise. The spatial variation of the dust spectral parameters (spectral index β and temperature T) in our simulations lead to significant biases on r (~21 σ r ) if not properly taken into account. Performing the moment expansion in β, as in previous studies, reduces the bias but does not lead to sufficiently reliable estimates of r. We introduce, for the first time, the expansion of the cross-angular power spectra SED in both β and T, showing that, at the sensitivity of LiteBIRD, the SED complexity due to temperature variations needs to be taken into account in order to prevent analysis biases on r. Thanks to this expansion, and despite the existing correlations between some of the dust moments and the CMB signal responsible for a rise in the error on r, we can measure an unbiased value of the tensor-to-scalar ratio with a dispersion as low as σ r = 8.8 × 10 –4 .

79 ASTRONOMY AND ASTROPHYSICS↗

Optical Characterization of the Keck Array and BICEP3 CMB Polarimeters from 2016 to 2019

The BICEP/Keck experiment (BK) is a series of small-aperture refracting telescopes observing degree-scale cosmic microwave background (CMB) polarization from the South Pole in search of a primordial B-mode signature. This B-mode signal arises from primordial gravitational waves interacting with the CMB and has amplitude parametrized by the tensor-to-scalar ratio r. Since 2016, BICEP3 and the Keck Array have been observing with 4800 total antenna-coupled transition-edge sensor detectors, with frequency bands spanning 95, 150, 220, and 270 GHz. Here we present the optical performance of these receivers from 2016 to 2019, including far-field beams measured in situ with an improved chopped thermal source and instrument spectral response measured with a field-deployable Fourier transform spectrometer. As a pair differencing experiment, an important systematic that must be controlled is the differential beam response between the co-located, orthogonally polarized detectors. We generate per-detector far-field beam maps and the corresponding differential beam mismatch that is used to estimate the temperature-to-polarization leakage in our CMB maps and to give feedback on detector and optics fabrication. The differential beam parameters presented here were estimated using improved low-level beam map analysis techniques, including efficient removal of non-Gaussian noise as well as improved spatial masking. These techniques help minimize systematic uncertainty in the beam analysis, with the goal of constraining the bias on r induced by temperature-to-polarization leakage to be subdominant to the statistical uncertainty. This is essential as we progress to higher detector counts in the next generation of CMB experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

CMB Lensing Reconstruction Using Two Years of Temperature Data from the SPT-3G Summer Survey

We present the first reconstruction of the cosmic microwave background (CMB) lensing potential from the SPT-3G Summer survey using two years of temperature data. The Summer survey has a total area of approximately 2640 deg$^2$, split into three fields covering 1210, 570, and 860 deg$^2$, respectively. A joint analysis of the three Summer fields yields a lensing amplitude of $A^{\rm comb} = 1.015 \pm 0.053$ relative to a fiducial Planck 2018 $Λ$CDM cosmology for the multipole range $50 < L < 2000$. These early results from the SPT-3G Summer survey highlight the potential for increasing the signal-to-noise ratio when combining the Summer fields with the SPT-3G Main and Wide fields for a total SPT-3G survey area of $\sim$ 10,000 deg$^2$.

Levy, K. [Melbourne U.]↗

BICEP/ K e c k XIV: Improved constraints on axionlike polarization oscillations in the cosmic microwave background

We present an improved search for axionlike polarization oscillations in the cosmic microwave background (CMB) with observations from the Keck Array . An all-sky, temporally sinusoidal rotation of CMB polarization, equivalent to a time-variable cosmic birefringence, is an observable manifestation of a local axion field and potentially allows a CMB polarimeter to detect axionlike dark matter directly. We describe improvements to the method presented in previous work, and we demonstrate the updated method with an expanded dataset consisting of the 2012–2015 observing seasons. We set limits on the axion-photon coupling constant for mass m in the range 10 - 23 – 10 - 18 eV , which corresponds to oscillation periods on the order of hours to years. Our results are consistent with the background model. For periods between 1 and 30 d ( 1.6 × 10 - 21 ≤ m ≤ 4.8 × 10 - 20 eV ), the 95%-confidence upper limits on rotation amplitude are approximately constant with a median of 0.27°, which constrains the axion-photon coupling constant to g φ γ < ( 4.5 × 10 - 12 GeV - 1 ) m / ( 10 - 21 eV ) , if axionlike particles constitute all of the dark matter. More than half of the collected BICEP dataset has yet to be analyzed, and several current and future CMB polarimetry experiments can apply the methods presented here to achieve comparable or superior constraints. In the coming years, oscillation measurements can achieve the sensitivity to rule out unexplored regions of the axion parameter space.

79 ASTRONOMY AND ASTROPHYSICS↗

Uncovering New Physics in the Cosmic Microwave Background: Developing Novel Theoretical Models and Machine-Learning-Powered Constraints

The search for evidence of new physics via its signatures in the cosmos is a cornerstone goal of the Office of High Energy Physics in the DOE Office of Science. Indeed, the current concordance cosmological model provides intriguing hints for beyond-the-standard-model (BSM) physics, such as dark matter and dark energy. Recently, a potential breakdown has appeared in this model, which could be initial evidence toward a further important revision in our fundamental theoretical understanding of cosmology. This breakdown is reflected in disagreements between inferences of the current expansion rate of the universe, H 0 (the Hubble constant), based on indirect, cosmological data (e.g., from the early universe) and based on direct, local measurements. Despite significant effort, a compelling new concordance cosmological model has yet to be found; achieving significant progress on this front was the first major focus of the project. Theoretical considerations indicate that if the observational discrepancies are not due to systematic errors, they strongly suggest new physics operating in the redshift range just prior to recombination, when cosmic microwave background (CMB) photons last scattered. Crucially, almost all such models produce unique signatures in the CMB temperature and polarization power spectra, which will be measured with unprecedented precision by ongoing and upcoming experiments, including the DOE-supported CMB-S4 project. However, these subtle hints of new physics must be uncovered from beneath a swath of Galactic and extragalactic foreground contamination. Current CMB analysis methods, although powerful, do not optimally infer the CMB power spectrum in the presence of non-Gaussian foregrounds. There is thus scope for theoretical improvement in this foundational challenge of cosmological inference, which formed the second major focus of the project. The primary objectives of the project were two-fold: (1) to develop new theoretical models in cosmology that can restore concordance amongst the full suite of cosmological data sets, thereby potentially providing evidence of novel BSM physics; (2) to develop new theoretical machinery to enable significant sensitivity improvements in searches for new physics in cosmology, particularly via the CMB power spectrum. The two objectives are intertwined, as the analysis methodology improvements in (2) will enable the tightest possible constraints on the signatures of new physics predicted by the novel scenarios in (1). The theoretical approaches to restore concordance focused on models involving novel scalar field dynamics in the pre-recombination universe (the “early dark energy” scenario and modifications thereof), as well as couplings between this field and other components in the standard cosmological model, such as dark matter. We also studied a model featuring a generalization of the decaying dark matter scenario, in which a sub-component of dark matter converts into dark radiation at late times in cosmic history. While these ideas are mostly driven by phenomenological considerations, this tactic has proven extremely successful in cosmology throughout the past few decades, including in the early history of evidence for dark matter and dark energy. The new theoretical machinery envisioned in (2) is undergirded by developments in signal processing and machine learning, which will enable improvements in CMB power spectrum estimation in the presence of non-Gaussian foreground contaminants. In turn, this will yield optimal sensitivity in searches for new physics in the CMB, by maximizing the cosmological information that is extracted from this observable. The most ambitious outcome of this work would be the construction of a new cosmological model that restores concordance amongst data sets. Although the individual models studied here did not fully achieve that goal, significant progress in narrowing down the model space was made, as described below. Moreover, the outcome of the methodological improvements in (2) will significantly impact a wide range of theoretical cosmology, by enabling the tightest possible constraints on any model that leaves novel signatures in the CMB temperature and polarization power spectra.

79 ASTRONOMY AND ASTROPHYSICS↗

Cross-correlating radial peculiar velocities and CMB lensing convergence

We study, for the first time, the cross correlation between the angular distribution of radial peculiar velocities (PV) and the lensing convergence of cosmic microwave background (CMB) photons. We derive theoretical expectations for the signal and its covariance and assess its detectability with existing and forthcoming surveys. We find that such cross-correlations are expected to improve constraints on different gravitational models by partially breaking degeneracies with the matter density. We identify in the distance-scaling dispersion of the peculiar velocities the most relevant source of noise in the cross correlation. For this reason, we also study how the above picture changes assuming a redshift-independent scatter for the PV, obtained for example using a reconstruction technique. Our results show that the cross correlation might be detected in the near future combining PV measurements from DESI and the convergence map from CMB-S4. Using realistic direct PV measurements we predict a cumulative signal-to-noise ratio of approximately 3.8σ using data on angular scales 3 ≤ ℓ ≤ 200. For an idealized reconstructed peculiar velocity map extending up to redshift z = 0.15 and a smoothing scale of 4 Mpc h -1 we predict a cumulative signal-to-noise ratio of approximately 27σ from angular scales 3 ≤ ℓ ≤ 200. We conclude that currently reconstructed peculiar velocities have more constraining power than directly observed ones, even though they are more cosmological-model dependent.

79 ASTRONOMY AND ASTROPHYSICS↗